Evaluating the Difference Quotient

AI Thread Summary
To evaluate the difference quotient for f(x) = x^3 at x = 1, the expression (f(1+h) - f(1)) / h simplifies to ((1+h)^3 - 1^3) / h. The correct simplification yields h^2 + 3h + 3, which is obtained without taking the limit as h approaches 0. The initial confusion stemmed from misinterpreting the problem as requiring the derivative rather than simply simplifying the difference quotient. After recalculating with the correct approach, the solution was confirmed as correct. Understanding the distinction between evaluating the difference quotient and finding the derivative is crucial in this context.
robertmatthew
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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.
 
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robertmatthew said:

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.
 
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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.
 

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