Use an algebraic strategy to verify that the point given for the function is either a maximum or minimum.

f(x) = x3 - 3x; (-1,2)

The answer should be 0 yet i get another answer. This is what i did:[COLOR=rgb(0, 0, 0)]

[/COLOR]$\displaystyle (a+h)-(a)/h=(-1+h)-(-1)/h=(-1+h)^3-(-3(-1))/h$

$\displaystyle (-1+h)(-1+h)(-1+h)=(1-h-h+h^2)(-1+h)=-1+3h-3h^2+h^3$

$\displaystyle (-1+3h-3h^2+h^3-3/h$

"h's" cancel

$\displaystyle -1+3-3h+h^2-3=h^2-3h-1$

$\displaystyle h=0.01,h=-0.01$

$\displaystyle (0.01)^2-3(0.01)-1=-1.0299$

$\displaystyle (-0.01)^2-3(-0.01)-1=-0.9699$

$\displaystyle -1.0299+(-0.9699)/2=-0.9999$

It should = 0 however and the slopes should be negative right side and positive left side I believe proving it is a maximum.