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, $\displaystyle f'(x) = \lim_{h \to 0} \frac {f(x + h) - f(x)}h$ or equivalently, $\displaystyle f'(a) = \lim_{x \to a} \frac {f(x) - f(a)}{x - a}$
Use either definition along with the $\displaystyle \epsilon - \delta$ 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, $\displaystyle \lim_{x \to 2} \frac {x^3 - 3x + 6 - 8}{x - 2} = \lim_{x \to 2} \frac {x^3 - 3x - 2}{x - 2} = 9$