Precalculus Examples

$c (x) = 10 e^{0.02 x}$

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.

$c (x + h) = 10 e^{0.02 (x + h)}$

Step 2.1.2

Simplify the result.

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Step 2.1.2.1

Apply the distributive property.

$c (x + h) = 10 e^{0.02 x + 0.02 h}$

Step 2.1.2.2

The final answer is $10 e^{0.02 x + 0.02 h}$ .

$10 e^{0.02 x + 0.02 h}$

Step 2.2

Find the components of the definition.

$c (x + h) = 10 e^{0.02 x + 0.02 h}$

$c (x) = 10 e^{0.02 x}$

$c (x + h) = 10 e^{0.02 x + 0.02 h}$

$c (x) = 10 e^{0.02 x}$

Step 3

Plug in the components.

$\frac{c (x + h) - c x}{h} = \frac{10 e^{0.02 x + 0.02 h} - (10 e^{0.02 x})}{h}$

Step 4

Simplify the numerator.

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Step 4.1

Multiply $- 1$ by $10$ .

$\frac{10 e^{0.02 x + 0.02 h} - 10 e^{0.02 x}}{h}$

Step 4.2

Factor $10$ out of $10 e^{0.02 x + 0.02 h} - 10 e^{0.02 x}$ .

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Step 4.2.1

Factor $10$ out of $10 e^{0.02 x + 0.02 h}$ .

$\frac{10 e^{0.02 x + 0.02 h} - 10 e^{0.02 x}}{h}$

Step 4.2.2

Factor $10$ out of $- 10 e^{0.02 x}$ .

$\frac{10 e^{0.02 x + 0.02 h} + 10 (- e^{0.02 x})}{h}$

Step 4.2.3

Factor $10$ out of $10 e^{0.02 x + 0.02 h} + 10 (- e^{0.02 x})$ .

$\frac{10 (e^{0.02 x + 0.02 h} - e^{0.02 x})}{h}$

Step 5