Question

find the difference quotient of f; that is, find $\frac{f(x + h)-f(x)}{h}$, h $
eq$ 0, for the following function. f(x) = $sqrt{15x}$ $\frac{f(x + h)-f(x)}{h}$ = (simplify your answer.)

Explanation:

Step1: Find f(x + h)

$f(x+h)=\sqrt{15(x + h)}=\sqrt{15x+15h}$

Step2: Substitute f(x + h) and f(x) into the difference - quotient formula

$\frac{f(x + h)-f(x)}{h}=\frac{\sqrt{15x + 15h}-\sqrt{15x}}{h}$

Step3: Rationalize the numerator

Multiply the numerator and denominator by $\sqrt{15x + 15h}+\sqrt{15x}$

$$
LATEXBLOCK0
$$

Step4: Simplify the expression

Cancel out the h terms: $\frac{15}{\sqrt{15x + 15h}+\sqrt{15x}}$

Answer:

$\frac{15}{\sqrt{15x + 15h}+\sqrt{15x}}$