Let , where is a real…

MATHEMATICS · Multi-part · A Level · Mathematics · Differentiation · Differentiation

Problem

Let

h_a(x)=x^{4}-4a x^{2}+16

, where

a

is a real parameter. (a) Compute

h_a'(x)

and find every critical point in terms of

a

. Assume all work is shown. (b) Determine all real values of

a

for which

h_a

has exactly two distinct relative extrema. Provide algebraic justification based on the sign of

h_a'(x)

. (c) For the values of

a

found in part (b), classify each extremum as a relative maximum or a relative minimum and state its

x

-coordinate.