Derivative f(x)=x^3, f(a+h)-f(a)/h

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Homework Help Overview

The discussion revolves around the derivative of the function f(x) = x^3, specifically focusing on the expression (f(a+h) - f(a))/h. Participants are exploring the simplification of this expression and its implications for finding the derivative.

Discussion Character

  • Exploratory, Mathematical reasoning, Problem interpretation

Approaches and Questions Raised

  • Participants are attempting to simplify the expression and clarify whether they are looking for the derivative or merely simplifying the equation. Some express confusion about the process and seek assistance with their calculations.

Discussion Status

There appears to be a mix of attempts to simplify the expression and discussions about the derivative. Some participants confirm the simplification provided, while others suggest using the limit definition of the derivative. The conversation is ongoing, with no clear consensus on the primary focus of the discussion.

Contextual Notes

Some participants mention the need to consider the limit as h approaches 0 for the derivative, while others indicate they are only interested in simplification. There is a reference to differing educational approaches to the problem.

alexhenderson
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Homework Statement



f(x)=x^3 f(a+h)-f(a)/h

Homework Equations


I am having troubles at the moment with the process, I am getting a^3+3a^2h+3ah^2+h^3-a^3.

The Attempt at a Solution



I have simplified the equation further and got 3a^2+3ah+h^2, help would be appreciated. Thanks for reading.
 
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You are trying to look for the derivative? Or just simplifying the equation?

You will need to get the limit as h approaches 0 for derivative.
 
Lily@pie said:
You are trying to look for the derivative? Or just simplifying the equation?

I already know the derivative, so just simplifying the equation.
 
If you just need to simplify the equation f(a+h)-f(a)/h, then you have already done so by getting 3a^2+3ah+h^2 as the answer.
 
Lily@pie said:
If you just need to simplify the equation f(a+h)-f(a)/h, then you have already done so by getting 3a^2+3ah+h^2 as the answer.

http://img192.imageshack.us/f/derivative.jpg/" Can you check my math? Please.
 
Last edited by a moderator:
It should be fine... According to my education system ><

For me, i'll straight away use the definition of derivative
f'(x) = limh->0 f(a+h)-f(a)/h

Would not try to derive all the way from (f(b)-f(a))/(b-a), too time consuming.
 
Ok, thank you.
 

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