Question

8.3 rates of change and behavior of graphs
core: 14.26/22 answered: 17/22
question 18
find the difference quotient $\frac{f(x + h)-f(x)}{h}$, $h
eq0$, for the given function $f$.
f(x)=15x - 2
question help: written example
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Explanation:

Step1: Find f(x + h)

Substitute x + h into f(x):
$f(x + h)=15(x + h)-2=15x+15h - 2$

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

$\frac{f(x + h)-f(x)}{h}=\frac{(15x + 15h-2)-(15x - 2)}{h}$

Step3: Simplify the numerator

$(15x + 15h-2)-(15x - 2)=15x+15h - 2-15x + 2=15h$

Step4: Simplify the fraction

$\frac{15h}{h}=15$

Answer:

15