Question

2.7
score: 20/25 answered: 20/25
question 21
find the difference quotient $\frac{f(x + h)-f(x)}{h},h
eq0$, for the given function $f$.
f(x)=4x + 1
question help: video ebook

Explanation:

Step1: Find $f(x + h)$

Substitute $x+h$ into $f(x)$:
$f(x + h)=4(x + h)+1=4x+4h + 1$

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

$f(x + h)-f(x)=(4x + 4h+1)-(4x + 1)=4x+4h + 1-4x - 1=4h$

Step3: Find the difference quotient

$\frac{f(x + h)-f(x)}{h}=\frac{4h}{h}=4$

Answer:

$4$