Precalculus Examples

$h (w) = 0.11 w^{1.36}$

Step 1

Consider the difference quotient formula.

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

Step 2

Find the components of the definition.

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Step 2.1

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

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Step 2.1.1

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

$h (w + h) = 0.11 {(w + h)}^{1.36}$

Step 2.1.2

The final answer is $0.11 {(w + h)}^{1.36}$ .

$0.11 {(w + h)}^{1.36}$

Step 2.2

Find the components of the definition.

$h (w + h) = 0.11 {(w + h)}^{1.36}$

$h (w) = 0.11 w^{1.36}$

$h (w + h) = 0.11 {(w + h)}^{1.36}$

$h (w) = 0.11 w^{1.36}$

Step 3

Plug in the components.

$\frac{h (w + h) - h w}{h} = \frac{0.11 {(w + h)}^{1.36} - (0.11 w^{1.36})}{h}$

Step 4

Simplify the numerator.

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Step 4.1

Factor $0.01$ out of $0.11 {(w + h)}^{1.36} - 1 \cdot 0.11 w^{1.36}$ .

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Step 4.1.1

Factor $0.01$ out of $0.11 {(w + h)}^{1.36}$ .

$\frac{0.01 (11 {(w + h)}^{1.36}) - 1 \cdot 0.11 w^{1.36}}{h}$

Step 4.1.2

Factor $0.01$ out of $- 1 \cdot 0.11 w^{1.36}$ .

$\frac{0.01 (11 {(w + h)}^{1.36}) + 0.01 (- 100 \cdot 0.11 w^{1.36})}{h}$

Step 4.1.3

Factor $0.01$ out of $0.01 (11 {(w + h)}^{1.36}) + 0.01 (- 100 \cdot 0.11 w^{1.36})$ .

$\frac{0.01 (11 {(w + h)}^{1.36} - 100 \cdot 0.11 w^{1.36})}{h}$

Step 4.2

Multiply $- 100$ by $0.11$ .

$\frac{0.01 (11 {(w + h)}^{1.36} - 11 w^{1.36})}{h}$

Step 4.3

Factor $11$ out of $11 {(w + h)}^{1.36} - 11 w^{1.36}$ .

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Step 4.3.1

Factor $11$ out of $- 11 w^{1.36}$ .

$\frac{0.01 (11 {(w + h)}^{1.36} + 11 (- w^{1.36}))}{h}$

Step 4.3.2

Factor $11$ out of $11 {(w + h)}^{1.36} + 11 (- w^{1.36})$ .

$\frac{0.01 (11 ({(w + h)}^{1.36} - w^{1.36}))}{h}$

$\frac{0.01 \cdot 11 ({(w + h)}^{1.36} - w^{1.36})}{h}$

Step 4.4

Multiply $0.01$ by $11$ .

$\frac{0.11 ({(w + h)}^{1.36} - w^{1.36})}{h}$

Step 5