Calculus Examples

$f (x) = \frac{10}{3} x^{3} - \frac{41}{2} x^{2} + 4 x + 6$

Step 1

Find the first derivative.

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Step 1.1

Find the first derivative.

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Step 1.1.1

By the Sum Rule, the derivative of $\frac{10}{3} x^{3} - \frac{41}{2} x^{2} + 4 x + 6$ with respect to $x$ is $\frac{d}{d x} [\frac{10}{3} x^{3}] + \frac{d}{d x} [- \frac{41}{2} x^{2}] + \frac{d}{d x} [4 x] + \frac{d}{d x} [6]$ .

$\frac{d}{d x} [\frac{10}{3} x^{3}] + \frac{d}{d x} [- \frac{41}{2} x^{2}] + \frac{d}{d x} [4 x] + \frac{d}{d x} [6]$

Step 1.1.2

Evaluate $\frac{d}{d x} [\frac{10}{3} x^{3}]$ .

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Step 1.1.2.1

Since $\frac{10}{3}$ is constant with respect to $x$ , the derivative of $\frac{10}{3} x^{3}$ with respect to $x$ is $\frac{10}{3} \frac{d}{d x} [x^{3}]$ .

$\frac{10}{3} \frac{d}{d x} [x^{3}] + \frac{d}{d x} [- \frac{41}{2} x^{2}] + \frac{d}{d x} [4 x] + \frac{d}{d x} [6]$

Step 1.1.2.2

Differentiate using the Power Rule which states that $\frac{d}{d x} [x^{n}]$ is $n x^{n - 1}$ where $n = 3$ .

$\frac{10}{3} (3 x^{2}) + \frac{d}{d x} [- \frac{41}{2} x^{2}] + \frac{d}{d x} [4 x] + \frac{d}{d x} [6]$

Step 1.1.2.3

Combine $3$ and $\frac{10}{3}$ .

$\frac{3 \cdot 10}{3} x^{2} + \frac{d}{d x} [- \frac{41}{2} x^{2}] + \frac{d}{d x} [4 x] + \frac{d}{d x} [6]$

Step 1.1.2.4

Multiply $3$ by $10$ .

$\frac{30}{3} x^{2} + \frac{d}{d x} [- \frac{41}{2} x^{2}] + \frac{d}{d x} [4 x] + \frac{d}{d x} [6]$

Step 1.1.2.5

Combine $\frac{30}{3}$ and $x^{2}$ .

$\frac{30 x^{2}}{3} + \frac{d}{d x} [- \frac{41}{2} x^{2}] + \frac{d}{d x} [4 x] + \frac{d}{d x} [6]$

Step 1.1.2.6

Cancel the common factor of $30$ and $3$ .

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Step 1.1.2.6.1

Factor $3$ out of $30 x^{2}$ .

$\frac{3 (10 x^{2})}{3} + \frac{d}{d x} [- \frac{41}{2} x^{2}] + \frac{d}{d x} [4 x] + \frac{d}{d x} [6]$

Step 1.1.2.6.2

Cancel the common factors.

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Step 1.1.2.6.2.1

Factor $3$ out of $3$ .

$\frac{3 (10 x^{2})}{3 (1)} + \frac{d}{d x} [- \frac{41}{2} x^{2}] + \frac{d}{d x} [4 x] + \frac{d}{d x} [6]$

Step 1.1.2.6.2.2

Cancel the common factor.

$\frac{3 (10 x^{2})}{3 \cdot 1} + \frac{d}{d x} [- \frac{41}{2} x^{2}] + \frac{d}{d x} [4 x] + \frac{d}{d x} [6]$

Step 1.1.2.6.2.3

Rewrite the expression.

$\frac{10 x^{2}}{1} + \frac{d}{d x} [- \frac{41}{2} x^{2}] + \frac{d}{d x} [4 x] + \frac{d}{d x} [6]$

Step 1.1.2.6.2.4

Divide $10 x^{2}$ by $1$ .

$10 x^{2} + \frac{d}{d x} [- \frac{41}{2} x^{2}] + \frac{d}{d x} [4 x] + \frac{d}{d x} [6]$

Step 1.1.3

Evaluate $\frac{d}{d x} [- \frac{41}{2} x^{2}]$ .

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Step 1.1.3.1

Since $- \frac{41}{2}$ is constant with respect to $x$ , the derivative of $- \frac{41}{2} x^{2}$ with respect to $x$ is $- \frac{41}{2} \frac{d}{d x} [x^{2}]$ .

$10 x^{2} - \frac{41}{2} \frac{d}{d x} [x^{2}] + \frac{d}{d x} [4 x] + \frac{d}{d x} [6]$

Step 1.1.3.2

Differentiate using the Power Rule which states that $\frac{d}{d x} [x^{n}]$ is $n x^{n - 1}$ where $n = 2$ .

$10 x^{2} - \frac{41}{2} (2 x) + \frac{d}{d x} [4 x] + \frac{d}{d x} [6]$

Step 1.1.3.3

Multiply $2$ by $- 1$ .

$10 x^{2} - 2 (\frac{41}{2}) x + \frac{d}{d x} [4 x] + \frac{d}{d x} [6]$

Step 1.1.3.4

Combine $- 2$ and $\frac{41}{2}$ .

$10 x^{2} + \frac{- 2 \cdot 41}{2} x + \frac{d}{d x} [4 x] + \frac{d}{d x} [6]$

Step 1.1.3.5

Multiply $- 2$ by $41$ .

$10 x^{2} + \frac{- 82}{2} x + \frac{d}{d x} [4 x] + \frac{d}{d x} [6]$

Step 1.1.3.6

Combine $\frac{- 82}{2}$ and $x$ .

$10 x^{2} + \frac{- 82 x}{2} + \frac{d}{d x} [4 x] + \frac{d}{d x} [6]$

Step 1.1.3.7

Cancel the common factor of $- 82$ and $2$ .

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Step 1.1.3.7.1

Factor $2$ out of $- 82 x$ .

$10 x^{2} + \frac{2 (- 41 x)}{2} + \frac{d}{d x} [4 x] + \frac{d}{d x} [6]$

Step 1.1.3.7.2

Cancel the common factors.

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Step 1.1.3.7.2.1

Factor $2$ out of $2$ .

$10 x^{2} + \frac{2 (- 41 x)}{2 (1)} + \frac{d}{d x} [4 x] + \frac{d}{d x} [6]$

Step 1.1.3.7.2.2

Cancel the common factor.

$10 x^{2} + \frac{2 (- 41 x)}{2 \cdot 1} + \frac{d}{d x} [4 x] + \frac{d}{d x} [6]$

Step 1.1.3.7.2.3

Rewrite the expression.

$10 x^{2} + \frac{- 41 x}{1} + \frac{d}{d x} [4 x] + \frac{d}{d x} [6]$

Step 1.1.3.7.2.4

Divide $- 41 x$ by $1$ .

$10 x^{2} - 41 x + \frac{d}{d x} [4 x] + \frac{d}{d x} [6]$

Step 1.1.4

Evaluate $\frac{d}{d x} [4 x]$ .

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Step 1.1.4.1

Since $4$ is constant with respect to $x$ , the derivative of $4 x$ with respect to $x$ is $4 \frac{d}{d x} [x]$ .

$10 x^{2} - 41 x + 4 \frac{d}{d x} [x] + \frac{d}{d x} [6]$

Step 1.1.4.2

Differentiate using the Power Rule which states that $\frac{d}{d x} [x^{n}]$ is $n x^{n - 1}$ where $n = 1$ .

$10 x^{2} - 41 x + 4 \cdot 1 + \frac{d}{d x} [6]$

Step 1.1.4.3

Multiply $4$ by $1$ .

$10 x^{2} - 41 x + 4 + \frac{d}{d x} [6]$

Step 1.1.5

Differentiate using the Constant Rule.

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Step 1.1.5.1

Since $6$ is constant with respect to $x$ , the derivative of $6$ with respect to $x$ is $0$ .

$10 x^{2} - 41 x + 4 + 0$

Step 1.1.5.2

Add $10 x^{2} - 41 x + 4$ and $0$ .

$f' (x) = 10 x^{2} - 41 x + 4$

Step 1.2

The first derivative of $f (x)$ with respect to $x$ is $10 x^{2} - 41 x + 4$ .

$10 x^{2} - 41 x + 4$

Step 2

Set the first derivative equal to $0$ then solve the equation $10 x^{2} - 41 x + 4 = 0$ .

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Step 2.1

Set the first derivative equal to $0$ .

$10 x^{2} - 41 x + 4 = 0$

Step 2.2

Factor by grouping.

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Step 2.2.1

For a polynomial of the form $a x^{2} + b x + c$ , rewrite the middle term as a sum of two terms whose product is $a \cdot c = 10 \cdot 4 = 40$ and whose sum is $b = - 41$ .

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Step 2.2.1.1

Factor $- 41$ out of $- 41 x$ .

$10 x^{2} - 41 x + 4 = 0$

Step 2.2.1.2

Rewrite $- 41$ as $- 1$ plus $- 40$

$10 x^{2} + (- 1 - 40) x + 4 = 0$

Step 2.2.1.3

Apply the distributive property.

$10 x^{2} - 1 x - 40 x + 4 = 0$

Step 2.2.2

Factor out the greatest common factor from each group.

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Step 2.2.2.1

Group the first two terms and the last two terms.

$(10 x^{2} - 1 x) - 40 x + 4 = 0$

Step 2.2.2.2

Factor out the greatest common factor (GCF) from each group.

$x (10 x - 1) - 4 (10 x - 1) = 0$

Step 2.2.3

Factor the polynomial by factoring out the greatest common factor, $10 x - 1$ .

$(10 x - 1) (x - 4) = 0$

Step 2.3

If any individual factor on the left side of the equation is equal to $0$ , the entire expression will be equal to $0$ .

$10 x - 1 = 0$

$x - 4 = 0$

Step 2.4

Set $10 x - 1$ equal to $0$ and solve for $x$ .

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Step 2.4.1

Set $10 x - 1$ equal to $0$ .

$10 x - 1 = 0$

Step 2.4.2

Solve $10 x - 1 = 0$ for $x$ .

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Step 2.4.2.1

Add $1$ to both sides of the equation.

$10 x = 1$

Step 2.4.2.2

Divide each term in $10 x = 1$ by $10$ and simplify.

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Step 2.4.2.2.1

Divide each term in $10 x = 1$ by $10$ .

$\frac{10 x}{10} = \frac{1}{10}$

Step 2.4.2.2.2

Simplify the left side.

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Step 2.4.2.2.2.1

Cancel the common factor of $10$ .

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Step 2.4.2.2.2.1.1

Cancel the common factor.

$\frac{10 x}{10} = \frac{1}{10}$

Step 2.4.2.2.2.1.2

Divide $x$ by $1$ .

$x = \frac{1}{10}$

Step 2.5

Set $x - 4$ equal to $0$ and solve for $x$ .

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Step 2.5.1

Set $x - 4$ equal to $0$ .

$x - 4 = 0$

Step 2.5.2

Add $4$ to both sides of the equation.

$x = 4$

Step 2.6

The final solution is all the values that make $(10 x - 1) (x - 4) = 0$ true.

$x = \frac{1}{10}, 4$

Step 3

Find the values where the derivative is undefined.

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Step 3.1

The domain of the expression is all real numbers except where the expression is undefined. In this case, there is no real number that makes the expression undefined.

Step 4

Evaluate $\frac{10}{3} x^{3} - \frac{41}{2} x^{2} + 4 x + 6$ at each $x$ value where the derivative is $0$ or undefined.

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Step 4.1

Evaluate at $x = \frac{1}{10}$ .

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Step 4.1.1

Substitute $\frac{1}{10}$ for $x$ .

$\frac{10}{3} \cdot {(\frac{1}{10})}^{3} - \frac{41}{2} \cdot {(\frac{1}{10})}^{2} + 4 (\frac{1}{10}) + 6$

Step 4.1.2

Simplify.

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Step 4.1.2.1

Simplify each term.

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Step 4.1.2.1.1

Apply the product rule to $\frac{1}{10}$ .

$\frac{10}{3} \cdot \frac{1^{3}}{10^{3}} - \frac{41}{2} \cdot {(\frac{1}{10})}^{2} + 4 (\frac{1}{10}) + 6$

Step 4.1.2.1.2

Combine.

$\frac{10 \cdot 1^{3}}{3 \cdot 10^{3}} - \frac{41}{2} \cdot {(\frac{1}{10})}^{2} + 4 (\frac{1}{10}) + 6$

Step 4.1.2.1.3

Cancel the common factor of $10$ and $10^{3}$ .

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Step 4.1.2.1.3.1

Factor $10$ out of $10 \cdot 1^{3}$ .

$\frac{10 (1^{3})}{3 \cdot 10^{3}} - \frac{41}{2} \cdot {(\frac{1}{10})}^{2} + 4 (\frac{1}{10}) + 6$

Step 4.1.2.1.3.2

Cancel the common factors.

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Step 4.1.2.1.3.2.1

Factor $10$ out of $3 \cdot 10^{3}$ .

$\frac{10 (1^{3})}{10 \cdot 3 \cdot 10^{2}} - \frac{41}{2} \cdot {(\frac{1}{10})}^{2} + 4 (\frac{1}{10}) + 6$

Step 4.1.2.1.3.2.2

Cancel the common factor.

$\frac{10 \cdot 1^{3}}{10 \cdot 3 \cdot 10^{2}} - \frac{41}{2} \cdot {(\frac{1}{10})}^{2} + 4 (\frac{1}{10}) + 6$

Step 4.1.2.1.3.2.3

Rewrite the expression.

$\frac{1^{3}}{3 \cdot 10^{2}} - \frac{41}{2} \cdot {(\frac{1}{10})}^{2} + 4 (\frac{1}{10}) + 6$

Step 4.1.2.1.4

One to any power is one.

$\frac{1}{3 \cdot 10^{2}} - \frac{41}{2} \cdot {(\frac{1}{10})}^{2} + 4 (\frac{1}{10}) + 6$

Step 4.1.2.1.5

Divide using scientific notation.

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Step 4.1.2.1.5.1

Group coefficients together and exponents together to divide numbers in scientific notation.

$(\frac{1}{3}) (\frac{1}{10^{2}}) - \frac{41}{2} \cdot {(\frac{1}{10})}^{2} + 4 (\frac{1}{10}) + 6$

Step 4.1.2.1.5.2

Divide $1$ by $3$ .

$0.\overline{3} \frac{1}{10^{2}} - \frac{41}{2} \cdot {(\frac{1}{10})}^{2} + 4 (\frac{1}{10}) + 6$

Step 4.1.2.1.5.3

Move $10^{2}$ to the numerator using the negative exponent rule $\frac{1}{b^{n}} = b^{- n}$ .

$0.\overline{3} \cdot 10^{- 2} - \frac{41}{2} \cdot {(\frac{1}{10})}^{2} + 4 (\frac{1}{10}) + 6$

Step 4.1.2.1.6

Move the decimal point in $0.\overline{3}$ to the right by $1$ place and decrease the power of $10^{- 2}$ by $1$ .

$3.\overline{3} \cdot 10^{- 3} - \frac{41}{2} \cdot {(\frac{1}{10})}^{2} + 4 (\frac{1}{10}) + 6$

Step 4.1.2.1.7

Apply the product rule to $\frac{1}{10}$ .

$3.\overline{3} \cdot 10^{- 3} - \frac{41}{2} \cdot \frac{1^{2}}{10^{2}} + 4 (\frac{1}{10}) + 6$

Step 4.1.2.1.8

One to any power is one.

$3.\overline{3} \cdot 10^{- 3} - \frac{41}{2} \cdot \frac{1}{10^{2}} + 4 (\frac{1}{10}) + 6$

Step 4.1.2.1.9

Raise $10$ to the power of $2$ .

$3.\overline{3} \cdot 10^{- 3} - \frac{41}{2} \cdot \frac{1}{100} + 4 (\frac{1}{10}) + 6$

Step 4.1.2.1.10

Multiply $- \frac{41}{2} \cdot \frac{1}{100}$ .

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Step 4.1.2.1.10.1

Multiply $\frac{1}{100}$ by $\frac{41}{2}$ .

$3.\overline{3} \cdot 10^{- 3} - \frac{41}{100 \cdot 2} + 4 (\frac{1}{10}) + 6$

Step 4.1.2.1.10.2

Multiply $100$ by $2$ .

$3.\overline{3} \cdot 10^{- 3} - \frac{41}{200} + 4 (\frac{1}{10}) + 6$

Step 4.1.2.1.11

Cancel the common factor of $2$ .

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Step 4.1.2.1.11.1

Factor $2$ out of $4$ .

$3.\overline{3} \cdot 10^{- 3} - \frac{41}{200} + 2 (2) \frac{1}{10} + 6$

Step 4.1.2.1.11.2

Factor $2$ out of $10$ .

$3.\overline{3} \cdot 10^{- 3} - \frac{41}{200} + 2 \cdot 2 \frac{1}{2 \cdot 5} + 6$

Step 4.1.2.1.11.3

Cancel the common factor.

$3.\overline{3} \cdot 10^{- 3} - \frac{41}{200} + 2 \cdot 2 \frac{1}{2 \cdot 5} + 6$

Step 4.1.2.1.11.4

Rewrite the expression.

$3.\overline{3} \cdot 10^{- 3} - \frac{41}{200} + 2 (\frac{1}{5}) + 6$

Step 4.1.2.1.12

Combine $2$ and $\frac{1}{5}$ .

$3.\overline{3} \cdot 10^{- 3} - \frac{41}{200} + \frac{2}{5} + 6$

Step 4.1.2.2

To write $\frac{2}{5}$ as a fraction with a common denominator, multiply by $\frac{40}{40}$ .

$3.\overline{3} \cdot 10^{- 3} - \frac{41}{200} + \frac{2}{5} \cdot \frac{40}{40} + 6$

Step 4.1.2.3

Write each expression with a common denominator of $200$ , by multiplying each by an appropriate factor of $1$ .

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Step 4.1.2.3.1

Multiply $\frac{2}{5}$ by $\frac{40}{40}$ .

$3.\overline{3} \cdot 10^{- 3} - \frac{41}{200} + \frac{2 \cdot 40}{5 \cdot 40} + 6$

Step 4.1.2.3.2

Multiply $5$ by $40$ .

$3.\overline{3} \cdot 10^{- 3} - \frac{41}{200} + \frac{2 \cdot 40}{200} + 6$

Step 4.1.2.4

Combine the numerators over the common denominator.

$3.\overline{3} \cdot 10^{- 3} + \frac{- 41 + 2 \cdot 40}{200} + 6$

Step 4.1.2.5

Simplify the numerator.

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Step 4.1.2.5.1

Multiply $2$ by $40$ .

$3.\overline{3} \cdot 10^{- 3} + \frac{- 41 + 80}{200} + 6$

Step 4.1.2.5.2

Add $- 41$ and $80$ .

$3.\overline{3} \cdot 10^{- 3} + \frac{39}{200} + 6$

Step 4.1.2.6

To write $6$ as a fraction with a common denominator, multiply by $\frac{200}{200}$ .

$3.\overline{3} \cdot 10^{- 3} + \frac{39}{200} + 6 \cdot \frac{200}{200}$

Step 4.1.2.7

Combine $6$ and $\frac{200}{200}$ .

$3.\overline{3} \cdot 10^{- 3} + \frac{39}{200} + \frac{6 \cdot 200}{200}$

Step 4.1.2.8

Combine the numerators over the common denominator.

$3.\overline{3} \cdot 10^{- 3} + \frac{39 + 6 \cdot 200}{200}$

Step 4.1.2.9

Simplify the numerator.

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Step 4.1.2.9.1

Multiply $6$ by $200$ .

$3.\overline{3} \cdot 10^{- 3} + \frac{39 + 1200}{200}$

Step 4.1.2.9.2

Add $39$ and $1200$ .

$3.\overline{3} \cdot 10^{- 3} + \frac{1239}{200}$

Step 4.2

Evaluate at $x = 4$ .

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Step 4.2.1

Substitute $4$ for $x$ .

$\frac{10}{3} \cdot {(4)}^{3} - \frac{41}{2} \cdot {(4)}^{2} + 4 (4) + 6$

Step 4.2.2

Simplify.

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Step 4.2.2.1

Simplify each term.

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Step 4.2.2.1.1

Raise $4$ to the power of $3$ .

$\frac{10}{3} \cdot 64 - \frac{41}{2} \cdot {(4)}^{2} + 4 (4) + 6$

Step 4.2.2.1.2

Multiply $\frac{10}{3} \cdot 64$ .

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Step 4.2.2.1.2.1

Combine $\frac{10}{3}$ and $64$ .

$\frac{10 \cdot 64}{3} - \frac{41}{2} \cdot {(4)}^{2} + 4 (4) + 6$

Step 4.2.2.1.2.2

Multiply $10$ by $64$ .

$\frac{640}{3} - \frac{41}{2} \cdot {(4)}^{2} + 4 (4) + 6$

Step 4.2.2.1.3

Raise $4$ to the power of $2$ .

$\frac{640}{3} - \frac{41}{2} \cdot 16 + 4 (4) + 6$

Step 4.2.2.1.4

Cancel the common factor of $2$ .

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Step 4.2.2.1.4.1

Move the leading negative in $- \frac{41}{2}$ into the numerator.

$\frac{640}{3} + \frac{- 41}{2} \cdot 16 + 4 (4) + 6$

Step 4.2.2.1.4.2

Factor $2$ out of $16$ .

$\frac{640}{3} + \frac{- 41}{2} \cdot (2 (8)) + 4 (4) + 6$

Step 4.2.2.1.4.3

Cancel the common factor.

$\frac{640}{3} + \frac{- 41}{2} \cdot (2 \cdot 8) + 4 (4) + 6$

Step 4.2.2.1.4.4

Rewrite the expression.

$\frac{640}{3} - 41 \cdot 8 + 4 (4) + 6$

Step 4.2.2.1.5

Multiply $- 41$ by $8$ .

$\frac{640}{3} - 328 + 4 (4) + 6$

Step 4.2.2.1.6

Multiply $4$ by $4$ .

$\frac{640}{3} - 328 + 16 + 6$

Step 4.2.2.2

Find the common denominator.

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Step 4.2.2.2.1

Write $- 328$ as a fraction with denominator $1$ .

$\frac{640}{3} + \frac{- 328}{1} + 16 + 6$

Step 4.2.2.2.2

Multiply $\frac{- 328}{1}$ by $\frac{3}{3}$ .

$\frac{640}{3} + \frac{- 328}{1} \cdot \frac{3}{3} + 16 + 6$

Step 4.2.2.2.3

Multiply $\frac{- 328}{1}$ by $\frac{3}{3}$ .

$\frac{640}{3} + \frac{- 328 \cdot 3}{3} + 16 + 6$

Step 4.2.2.2.4

Write $16$ as a fraction with denominator $1$ .

$\frac{640}{3} + \frac{- 328 \cdot 3}{3} + \frac{16}{1} + 6$

Step 4.2.2.2.5

Multiply $\frac{16}{1}$ by $\frac{3}{3}$ .

$\frac{640}{3} + \frac{- 328 \cdot 3}{3} + \frac{16}{1} \cdot \frac{3}{3} + 6$

Step 4.2.2.2.6

Multiply $\frac{16}{1}$ by $\frac{3}{3}$ .

$\frac{640}{3} + \frac{- 328 \cdot 3}{3} + \frac{16 \cdot 3}{3} + 6$

Step 4.2.2.2.7

Write $6$ as a fraction with denominator $1$ .

$\frac{640}{3} + \frac{- 328 \cdot 3}{3} + \frac{16 \cdot 3}{3} + \frac{6}{1}$

Step 4.2.2.2.8

Multiply $\frac{6}{1}$ by $\frac{3}{3}$ .

$\frac{640}{3} + \frac{- 328 \cdot 3}{3} + \frac{16 \cdot 3}{3} + \frac{6}{1} \cdot \frac{3}{3}$

Step 4.2.2.2.9

Multiply $\frac{6}{1}$ by $\frac{3}{3}$ .

$\frac{640}{3} + \frac{- 328 \cdot 3}{3} + \frac{16 \cdot 3}{3} + \frac{6 \cdot 3}{3}$

Step 4.2.2.3

Combine the numerators over the common denominator.

$\frac{640 - 328 \cdot 3 + 16 \cdot 3 + 6 \cdot 3}{3}$

Step 4.2.2.4

Simplify each term.

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Step 4.2.2.4.1

Multiply $- 328$ by $3$ .

$\frac{640 - 984 + 16 \cdot 3 + 6 \cdot 3}{3}$

Step 4.2.2.4.2

Multiply $16$ by $3$ .

$\frac{640 - 984 + 48 + 6 \cdot 3}{3}$

Step 4.2.2.4.3

Multiply $6$ by $3$ .

$\frac{640 - 984 + 48 + 18}{3}$

Step 4.2.2.5

Simplify the expression.

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Step 4.2.2.5.1

Subtract $984$ from $640$ .

$\frac{- 344 + 48 + 18}{3}$

Step 4.2.2.5.2

Add $- 344$ and $48$ .

$\frac{- 296 + 18}{3}$

Step 4.2.2.5.3

Add $- 296$ and $18$ .

$\frac{- 278}{3}$

Step 4.2.2.5.4

Move the negative in front of the fraction.

$- \frac{278}{3}$

Step 4.3

List all of the points.

$(\frac{1}{10}, 3.\overline{3} \cdot 10^{- 3} + \frac{1239}{200}), (4, - \frac{278}{3})$

Step 5