Finding the derivative using the limit defintion.

**alpha** · January 18th 2010, 10:05 AM

Can you help me with this please:

Using delta/epsilon methods show from definitions that if f(x)= x^3-3x+6 then f`(2)=9.

Thank you.

**Jhevon** · January 18th 2010, 10:11 AM

Originally Posted by alpha

Can you help me with this please:

Using delta/epsilon methods show from definitions that if f(x)= x^3-3x+6 then f`(2)=9.

Thank you.

By definition, $f'(x) = \lim_{h \to 0} \frac {f(x + h) - f(x)}h$ or equivalently, $f'(a) = \lim_{x \to a} \frac {f(x) - f(a)}{x - a}$

Use either definition along with the $\epsilon - \delta$ definition of a limit that I showed you how to deal with in your last thread.

You want to show, using the latter definition, for example, $\lim_{x \to 2} \frac {x^3 - 3x + 6 - 8}{x - 2} = \lim_{x \to 2} \frac {x^3 - 3x - 2}{x - 2} = 9$

**alpha** · January 18th 2010, 10:29 AM

I have no idea about this question. can you show me how it is done.

Thanks again.

**Jhevon** · January 18th 2010, 10:44 AM

Originally Posted by alpha

I have no idea about this question. can you show me how it is done.

Thanks again.

i already gave you an example of how to tackle problems like this in your last thread. how about you take a crack at it?

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