Precalculus Examples

$y = \frac{7}{2} x$

Step 1

Write $y = \frac{7}{2} x$ as a function.

$f (x) = \frac{7}{2} x$

Step 2

Consider the difference quotient formula.

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

Step 3

Find the components of the definition.

Tap for more steps...

Step 3.1

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

Tap for more steps...

Step 3.1.1

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

$f (x + h) = \frac{7}{2} \cdot (x + h)$

Step 3.1.2

Simplify the result.

Tap for more steps...

Step 3.1.2.1

Apply the distributive property.

$f (x + h) = \frac{7}{2} x + \frac{7}{2} h$

Step 3.1.2.2

Combine $\frac{7}{2}$ and $x$ .

$f (x + h) = \frac{7 x}{2} + \frac{7}{2} h$

Step 3.1.2.3

Combine $\frac{7}{2}$ and $h$ .

$f (x + h) = \frac{7 x}{2} + \frac{7 h}{2}$

Step 3.1.2.4

The final answer is $\frac{7 x}{2} + \frac{7 h}{2}$ .

$\frac{7 x}{2} + \frac{7 h}{2}$

Step 3.2

Find the components of the definition.

$f (x + h) = \frac{7 x}{2} + \frac{7 h}{2}$

$f (x) = \frac{7 x}{2}$

$f (x + h) = \frac{7 x}{2} + \frac{7 h}{2}$

$f (x) = \frac{7 x}{2}$

Step 4

Plug in the components.

$\frac{f (x + h) - f (x)}{h} = \frac{\frac{7 x}{2} + \frac{7 h}{2} - (\frac{7 x}{2})}{h}$

Step 5

Simplify.

Tap for more steps...

Step 5.1

Simplify the numerator.

Tap for more steps...

Step 5.1.1

Subtract $\frac{7 x}{2}$ from $\frac{7 x}{2}$ .

$\frac{\frac{7 h}{2} + 0}{h}$

Step 5.1.2

Add $\frac{7 h}{2}$ and $0$ .

$\frac{\frac{7 h}{2}}{h}$

Step 5.2

Multiply the numerator by the reciprocal of the denominator.

$\frac{7 h}{2} \cdot \frac{1}{h}$

Step 5.3

Cancel the common factor of $h$ .

Tap for more steps...

Step 5.3.1

Factor $h$ out of $7 h$ .

$\frac{h \cdot 7}{2} \cdot \frac{1}{h}$

Step 5.3.2

Cancel the common factor.

$\frac{h \cdot 7}{2} \cdot \frac{1}{h}$

Step 5.3.3

Rewrite the expression.

$\frac{7}{2}$

Step 6