Precalculus Examples

$\frac{f (4) - f (0)}{4 - 0}$

Step 1

Write $\frac{f (4) - f (0)}{4 - 0}$ as a function.

$f (x) = \frac{f (4) - f (0)}{4 - 0}$

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.

$f (x + h) = \frac{f (4) - f \cdot 0}{4 - 0}$

Step 3.1.2

Simplify the result.

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Step 3.1.2.1

Simplify the numerator.

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Step 3.1.2.1.1

Factor $f$ out of $f (4) - f \cdot 0$ .

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Step 3.1.2.1.1.1

Factor $f$ out of $- f \cdot 0$ .

$f (x + h) = \frac{f (4) + f (- 1 \cdot 0)}{4 - 0}$

Step 3.1.2.1.1.2

Factor $f$ out of $f (4) + f (- 1 \cdot 0)$ .

$f (x + h) = \frac{f (4 - 1 \cdot 0)}{4 - 0}$

Step 3.1.2.1.2

Multiply $- 1$ by $0$ .

$f (x + h) = \frac{f (4 + 0)}{4 - 0}$

Step 3.1.2.1.3

Add $4$ and $0$ .

$f (x + h) = \frac{f \cdot 4}{4 - 0}$

Step 3.1.2.2

Simplify the denominator.

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Step 3.1.2.2.1

Multiply $- 1$ by $0$ .

$f (x + h) = \frac{f \cdot 4}{4 + 0}$

Step 3.1.2.2.2

Add $4$ and $0$ .

$f (x + h) = \frac{f \cdot 4}{4}$

Step 3.1.2.3

Cancel the common factor of $4$ .

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Step 3.1.2.3.1

Cancel the common factor.

$f (x + h) = \frac{f \cdot 4}{4}$

Step 3.1.2.3.2

Divide $f$ by $1$ .

$f (x + h) = f$

Step 3.1.2.4

The final answer is $f$ .

$f$

Step 3.2

Find the components of the definition.

$f (x + h) = f$

$f (x) = f$

$f (x + h) = f$

$f (x) = f$

Step 4

Plug in the components.

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

Step 5

Simplify.

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Step 5.1

Subtract $f$ from $f$ .

$\frac{0}{h}$

Step 5.2

Divide $0$ by $h$ .

$0$

Step 6