# How do you find the stationary points for #f(x)=x^4# ?

##### 1 Answer

The stationary point is

The first task in finding stationary points is to find the critical points, that is, where

#f'(x)=4x^3# using the power rule

#4x^3=0#

#x=0# is the only solution

There are 2 ways to test for a stationary point, the First Derivative Test and the Second Derivative Test.

The First Derivative Test checks for a sign change in the first derivative: on the left the derivative is negative and on the right the derivative is positive, so this critical point is a minimum.

The Second Derivative Test checks for the sign of the second derivative:

#f''(x)=12x^2#

#f''(0)=0#

There is no sign, so the second derivative doesn't tell us anything in this case.

Since there are no other minimums and