How do you find the stationary points for #f(x)=x^4# ?
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
#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:
There is no sign, so the second derivative doesn't tell us anything in this case.
Since there are no other minimums and