find the difference quotient of f; that is, find (f(x + h) - f(x))/h, h ≠ 0, for the following function…
find the difference quotient of f; that is, find (f(x + h) - f(x))/h, h ≠ 0, for the following function. f(x)=4x + 4 (f(x + h) - f(x))/h = (simplify your answer.)
Answer
Explanation:
Step1: Find f(x + h)
Substitute x + h into f(x): $f(x + h)=4(x + h)+4=4x+4h + 4$
Step2: Calculate f(x + h)-f(x)
$f(x + h)-f(x)=(4x + 4h+4)-(4x + 4)$ $=4x+4h + 4-4x - 4=4h$
Step3: Find the difference - quotient
$\frac{f(x + h)-f(x)}{h}=\frac{4h}{h}$ Since $h\neq0$, we can cancel out h: $\frac{4h}{h}=4$
Answer:
4