Consider , where is real. Determine all real values of for which possesses exactly…

MATHEMATICS · Subjective · A Level · Mathematics · Differentiation · Differentiation

Problem

Consider

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

, where

k

is real. Determine all real values of

k

for which

h

possesses exactly three distinct critical points, and classify the critical point at

x=0

as a relative maximum or minimum.