Precalculus Examples

$f (x) = 9 x$ , $x = 2$

Consider the difference quotient formula. Use this formula to solve for the slope of the secant line $m_{s e c}$ .

$m_{s e c} = \frac{f (x + h) - f (x)}{h}$

Find the components of the definition.

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

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

$f (x + h) = 9 (x + h)$

Simplify the result.

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Apply the distributive property.

$f (x + h) = 9 x + 9 h$

The final answer is $9 x + 9 h$ .

$9 x + 9 h$

Find the components of the definition.

$f (x + h) = 9 x + 9 h$

$f (x) = 9 x$

$f (x + h) = 9 x + 9 h$

$f (x) = 9 x$

Plug in the components.

$\frac{f (x + h) - f (x)}{h} = \frac{9 x + 9 h - (9 x)}{h}$

Simplify.

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Simplify the numerator.

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Multiply $9$ by $- 1$ .

$\frac{9 x + 9 h - 9 x}{h}$

Subtract $9 x$ from $9 x$ .

$\frac{9 h + 0}{h}$

Add $9 h$ and $0$ .

$\frac{9 h}{h}$

Divide $9$ by $1$ .

$9$

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