question 3 of 13, step 1 of 1 given the following function, determine the difference quotient, $\frac{f(x +…
question 3 of 13, step 1 of 1 given the following function, determine the difference quotient, $\frac{f(x + h)-f(x)}{h}$. $f(x)=-4x - 5$
Answer
Explanation:
Step1: Find $f(x + h)$
Substitute $x+h$ into $f(x)$: $f(x + h)=-4(x + h)-5=-4x-4h - 5$
Step2: Calculate $f(x + h)-f(x)$
[ \begin{align*} f(x + h)-f(x)&=(-4x-4h - 5)-(-4x - 5)\ &=-4x-4h - 5 + 4x+5\ &=-4h \end{align*} ]
Step3: Compute the difference - quotient
[ \begin{align*} \frac{f(x + h)-f(x)}{h}&=\frac{-4h}{h}\ &=-4 \end{align*} ]
Answer:
$-4$