Calculus Examples

$f (x) = \frac{3 x (615)}{3 x}$

Step 1

Find the first derivative of the function.

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Step 1.1

Reduce the expression by cancelling the common factors.

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Step 1.1.1

Multiply $615$ by $3$ .

$\frac{d}{d x} [\frac{1845 x}{3 x}]$

Step 1.1.2

Cancel the common factor of $1845$ and $3$ .

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Step 1.1.2.1

Factor $3$ out of $1845 x$ .

$\frac{d}{d x} [\frac{3 (615 x)}{3 x}]$

Step 1.1.2.2

Cancel the common factors.

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Step 1.1.2.2.1

Factor $3$ out of $3 x$ .

$\frac{d}{d x} [\frac{3 (615 x)}{3 (x)}]$

Step 1.1.2.2.2

Cancel the common factor.

$\frac{d}{d x} [\frac{3 (615 x)}{3 x}]$

Step 1.1.2.2.3

Rewrite the expression.

$\frac{d}{d x} [\frac{615 x}{x}]$

Step 1.1.3

Cancel the common factor of $x$ .

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Step 1.1.3.1

Cancel the common factor.

$\frac{d}{d x} [\frac{615 x}{x}]$

Step 1.1.3.2

Divide $615$ by $1$ .

$\frac{d}{d x} [615]$

Step 1.2

Since $615$ is constant with respect to $x$ , the derivative of $615$ with respect to $x$ is $0$ .

$0$

Step 2

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

$f'' (x) = 0$

Step 3

To find the local maximum and minimum values of the function, set the derivative equal to $0$ and solve.

$0 = 0$

Step 4

Since there is no value of $x$ that makes the first derivative equal to $0$ , there are no local extrema.

No Local Extrema

Step 5

No Local Extrema

Step 6