# Finding the derivative using the limit defintion.

• January 18th 2010, 10:05 AM
alpha
Finding the derivative using the limit defintion.
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.
• January 18th 2010, 10:11 AM
Jhevon
Quote:

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, $\lim_{x \to 2} \frac {x^3 - 3x + 6 - 8}{x - 2} = \lim_{x \to 2} \frac {x^3 - 3x - 2}{x - 2} = 9$
• January 18th 2010, 10:29 AM
alpha