Mathematics

Problem

The function

h(x)=x^4-4x^2+1

has critical points where

h'(x)=0

. Which of the following correctly states the nature of these critical points? a) Local maxima at

x=\pm\sqrt{2}

and a local minimum at

x=0

b) Local minima at

x=\pm\sqrt{2}

only;

x=0

is not an extremum c) Local minima at

x=\pm\sqrt{2}

and a local maximum at

x=0

d) Local minima at

x=0

and

x=\pm\sqrt{2}