Precalculus Examples

$y = \sqrt{x}$ , $(0, 6)$

Step 1

Substitute using the average rate of change formula.

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Step 1.1

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.

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

Step 1.2

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

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

Step 2

Simplify the expression.

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Step 2.1

Simplify the numerator.

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Step 2.1.1

Rewrite $0$ as $0^{2}$ .

$\frac{\sqrt{6} - \sqrt{0^{2}}}{6 - (0)}$

Step 2.1.2

Pull terms out from under the radical, assuming positive real numbers.

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

Step 2.1.3

Multiply $- 1$ by $0$ .

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

Step 2.1.4

Add $\sqrt{6}$ and $0$ .

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

Step 2.2

Simplify the denominator.

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Step 2.2.1

Multiply $- 1$ by $0$ .

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

Step 2.2.2

Add $6$ and $0$ .

$\frac{\sqrt{6}}{6}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$\frac{\sqrt{6}}{6}$

Decimal Form:

$0.40824829 \dots$