Question

Find the local maxima and local minima, if any, of the following functions. Find the sum of the local maximum and the local minimum values for:
$g\left(x\right)=x^3-3x$

Answer 1

$g^{\prime }\left(x\right)=3x^2-3=3(x-1)(x+1)=0\Rightarrow x=-1,1$

$g^{\prime \prime }\left(x\right)=6x\Rightarrow g^{\prime \prime }(-1)=6\ast -1=-6$

Hence Local Maximum is at $x=-1$

and Local minimum is at $x=1$

Local Maximum + Local Minimum $=g(-1)+g\left(1\right)=(-1+3)+(1-3)=0$