Question

If f(x) = x3, evaluate the difference quotient

f(6 + h) − f(6) h

Answer 1

Correct question is;

If f(x) = x³, evaluate the difference quotient: [f(6 + h) − f(6)]/h

Answer:

h² + 108h + 18

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