Evaluating the Difference Quotient

[robertmatthew]

Homework Statement

Evaluate the difference quotient of:
f(1+h)-f(1) / h
if f(x)=x³
and simplify your answer.

Homework Equations

The Attempt at a Solution

I took the derivative of x³ to be 3x² and solved for when x=1 (given from the difference quotient) and got 3, but when I enter the value it's marked incorrect. Not sure what I'm doing wrong, unless I just interpreted the question the wrong way.

 

[pasmith]

Homework Statement

Evaluate the difference quotient of:
f(1+h)-f(1) / h
if f(x)=x³
and simplify your answer.

Homework Equations

The Attempt at a Solution

I took the derivative of x³ to be 3x² and solved for when x=1 (given from the difference quotient) and got 3, but when I enter the value it's marked incorrect. Not sure what I'm doing wrong, unless I just interpreted the question the wrong way.

Calculate $((1 + h)^3 - 1^3)/h$ and do not take the limit $h \to 0$.

 

[robertmatthew]

Ah, okay. Got h^2+3h+3, entered it and it was correct. Thanks! I'm not sure why I thought it was asking for the limit, guess I'm still a little fuzzy from the summer.