follow the step by step process to determine the difference quotient, $\frac{f(x + h)-f(x)}{h}$. f(x)=x² - 15x a. determine f(x + h). f(x + h)= (simplify your answer.) b. simplify the expression f(x + h)-f(x). f(x + h)-f(x)= (simplify your answer.) c. determine the difference quotient $\frac{f(x + h)-f(x)}{h}$. $\frac{f(x + h)-f(x)}{h}=$

Question

Accepted Answer

# Explanation:
## Step1: Find f(x + h)
Substitute $x+h$ into $f(x)$:
$$
\begin{align*}
f(x + h)&=(x + h)^2-15(x + h)\
&=x^{2}+2xh+h^{2}-15x-15h
\end{align*}
$$
## Step2: Calculate f(x + h) - f(x)
$$
\begin{align*}
f(x + h)-f(x)&=(x^{2}+2xh + h^{2}-15x-15h)-(x^{2}-15x)\
&=x^{2}+2xh+h^{2}-15x-15h - x^{2}+15x\
&=2xh+h^{2}-15h
\end{align*}
$$
## Step3: Determine the difference quotient
$$
\begin{align*}
\frac{f(x + h)-f(x)}{h}&=\frac{2xh+h^{2}-15h}{h}\
&=\frac{h(2x + h-15)}{h}\
&=2x+h - 15
\end{align*}
$$
# Answer:
a. $x^{2}+2xh+h^{2}-15x-15h$
b. $2xh+h^{2}-15h$
c. $2x+h - 15$

Sovi.AI - AI Math Tutor

QUESTION IMAGE

Question

Explanation:

Step1: Find f(x + h)

Step2: Calculate f(x + h) - f(x)

Step3: Determine the difference quotient

Answer: