find the difference quotient of f; that is, find (f(x + h)-f(x))/h, h≠0, for the following function. f(x)=6x…
find the difference quotient of f; that is, find (f(x + h)-f(x))/h, h≠0, for the following function. f(x)=6x + 2 (f(x + h)-f(x))/h = □ (simplify your answer.)
Answer
Explanation:
Step1: Find f(x + h)
Substitute x + h into f(x): $f(x + h)=6(x + h)+2=6x+6h + 2$
Step2: Calculate f(x + h) - f(x)
$f(x + h)-f(x)=(6x + 6h+2)-(6x + 2)=6x+6h + 2-6x - 2=6h$
Step3: Find the difference - quotient
$\frac{f(x + h)-f(x)}{h}=\frac{6h}{h}=6$
Answer:
6