Calculus Examples

$y = 3 x + 3 x^{2}$ , $(1, - 5)$

Step 1

Write $y = 3 x + 3 x^{2}$ as a function.

$f (x) = 3 x + 3 x^{2}$

Step 2

Check if the given point is on the graph of the given function.

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Step 2.1

Evaluate $f (x) = 3 x + 3 x^{2}$ at $x = 1$ .

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Step 2.1.1

Replace the variable $x$ with $1$ in the expression.

$f (1) = 3 (1) + 3 {(1)}^{2}$

Step 2.1.2

Simplify the result.

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Step 2.1.2.1

Simplify each term.

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Step 2.1.2.1.1

Multiply $3$ by $1$ .

$f (1) = 3 + 3 {(1)}^{2}$

Step 2.1.2.1.2

One to any power is one.

$f (1) = 3 + 3 \cdot 1$

Step 2.1.2.1.3

Multiply $3$ by $1$ .

$f (1) = 3 + 3$

Step 2.1.2.2

Add $3$ and $3$ .

$f (1) = 6$

Step 2.1.2.3

The final answer is $6$ .

$6$

Step 2.2

Since $6$ $\neq$ $- 5$ , the point is not on the graph.

The point is not on the graph

Step 3