Precalculus Examples

$g (t) = 240 {(0.75)}^{3}$

Step 1

Consider the difference quotient formula.

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

Step 2

Find the components of the definition.

Tap for more steps...

Step 2.1

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

Tap for more steps...

Step 2.1.1

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

$g (t + h) = 240 {(0.75)}^{3}$

Step 2.1.2

Simplify the result.

Tap for more steps...

Step 2.1.2.1

Raise $0.75$ to the power of $3$ .

$g (t + h) = 240 \cdot 0.421875$

Step 2.1.2.2

Multiply $240$ by $0.421875$ .

$g (t + h) = 101.25$

Step 2.1.2.3

The final answer is $101.25$ .

$101.25$

Step 2.2

Find the components of the definition.

$g (t + h) = 101.25$

$g (t) = 101.25$

$g (t + h) = 101.25$

$g (t) = 101.25$

Step 3

Plug in the components.

$\frac{g (t + h) - g t}{h} = \frac{101.25 - (101.25)}{h}$

Step 4

Simplify.

Tap for more steps...

Step 4.1

Simplify the numerator.

Tap for more steps...

Step 4.1.1

Multiply $- 1$ by $101.25$ .

$\frac{101.25 - 101.25}{h}$

Step 4.1.2

Subtract $101.25$ from $101.25$ .

$\frac{0}{h}$

Step 4.2

Divide $0$ by $h$ .

$0$

Step 5