Precalculus Examples

$- \frac{1}{2}$

Step 1

Write $- \frac{1}{2}$ as a function.

$f (x) = - \frac{1}{2}$

Step 2

Consider the difference quotient formula.

$\frac{f (x + h) - f (x)}{h}$

Step 3

Find the components of the definition.

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Step 3.1

Evaluate the function at $x = x + h$ .

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Step 3.1.1

Replace the variable $x$ with $x + h$ in the expression.

$f (x + h) = - \frac{1}{2}$

Step 3.1.2

The final answer is $- \frac{1}{2}$ .

$- \frac{1}{2}$

Step 3.2

Find the components of the definition.

$f (x + h) = - \frac{1}{2}$

$f (x) = - \frac{1}{2}$

$f (x + h) = - \frac{1}{2}$

$f (x) = - \frac{1}{2}$

Step 4

Plug in the components.

$\frac{f (x + h) - f (x)}{h} = \frac{- \frac{1}{2} - (- \frac{1}{2})}{h}$

Step 5

Simplify.

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Step 5.1

Simplify the numerator.

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Step 5.1.1

Multiply $- - \frac{1}{2}$ .

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Step 5.1.1.1

Multiply $- 1$ by $- 1$ .

$\frac{- \frac{1}{2} + 1 (\frac{1}{2})}{h}$

Step 5.1.1.2

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

$\frac{- \frac{1}{2} + \frac{1}{2}}{h}$

Step 5.1.2

Add $- \frac{1}{2}$ and $\frac{1}{2}$ .

$\frac{0}{h}$

Step 5.2

Divide $0$ by $h$ .

$0$

Step 6