Consider the function

MATHEMATICS · Subjective · AP · Calculus AB · Analytical Applications of Differentiation · Analytical Applications of Differentiation

Problem

h(x)=x^{4}+ax^{2}+1

, where

a

is a real parameter. Classify the point

x=0

for different values of

a

: (a) For which values of

a

x=0

a local maximum? (b) For which values of

a

x=0

a local minimum? (c) For which value(s) of

a

x=0

neither a maximum nor a minimum according to the second derivative criterion?