Precalculus Examples

$y = 6 x^{3}$ , $(1, 6)$ , $(0, 0)$

Step 1

Write $y = 6 x^{3}$ as a function.

$f (x) = 6 x^{3}$

Step 2

Substitute using the average rate of change formula.

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Step 2.1

The average rate of change of a function can be found by calculating the change in $y$ values of the two points divided by the change in $x$ values of the two points.

$\frac{f (1) - f (0)}{(1) - (0)}$

Step 2.2

Substitute the equation $y = 6 x^{3}$ for $f (1)$ and $f (0)$ , replacing $x$ in the function with the corresponding $x$ value.

$\frac{(6 {(1)}^{3}) - (6 {(0)}^{3})}{(1) - (0)}$

Step 3

Simplify the expression.

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Step 3.1

Simplify the numerator.

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Step 3.1.1

One to any power is one.

$\frac{6 \cdot 1 - 1 \cdot 6 \cdot 0^{3}}{1 - (0)}$

Step 3.1.2

Multiply $6$ by $1$ .

$\frac{6 - 1 \cdot 6 \cdot 0^{3}}{1 - (0)}$

Step 3.1.3

Multiply $- 1$ by $6$ .

$\frac{6 - 6 \cdot 0^{3}}{1 - (0)}$

Step 3.1.4

Raising $0$ to any positive power yields $0$ .

$\frac{6 - 6 \cdot 0}{1 - (0)}$

Step 3.1.5

Multiply $- 6$ by $0$ .

$\frac{6 + 0}{1 - (0)}$

Step 3.1.6

Add $6$ and $0$ .

$\frac{6}{1 - (0)}$

Step 3.2

Simplify the denominator.

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Step 3.2.1

Multiply $- 1$ by $0$ .

$\frac{6}{1 + 0}$

Step 3.2.2

Add $1$ and $0$ .

$\frac{6}{1}$

Step 3.3

Divide $6$ by $1$ .

$6$