Correct question is;
If f(x) = x³, evaluate the difference quotient: [f(6 + h) − f(6)]/h
Answer:
h² + 108h + 18
Step-by-step explanation:
We are given f(x) = x³
Thus;
f(6 + h) = (6 + h)³ = (36 + 12h + h²)(6 + h) = 216 + 72h + 6h² + 36h + 12h² + h³ = 216 + 108h + 18h² + h³
Then, f(6) = 6³ = 216
Thus;
[f(6 + h) − f(6)]/h = [216 + 108h + 18h² + h³ - 216]/h = (h³ + 108h + 18h²)/h
This gives;
h² + 108h + 18
