Precalculus Examples

$f (x) = 2 \cos (x) + 1$

Step 1

Consider the difference quotient formula.

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

Step 2

Find the components of the definition.

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Step 2.1

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

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Step 2.1.1

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

$f (x + h) = 2 \cos (x + h) + 1$

Step 2.1.2

The final answer is $2 \cos (x + h) + 1$ .

$2 \cos (x + h) + 1$

Step 2.2

Find the components of the definition.

$f (x + h) = 2 \cos (x + h) + 1$

$f (x) = 2 \cos (x) + 1$

$f (x + h) = 2 \cos (x + h) + 1$

$f (x) = 2 \cos (x) + 1$

Step 3

Plug in the components.

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

Step 4