Mathematics

Problem

Let

p_c(x)=x^4-4cx

be defined on the closed interval

[-2,3]

, where

c

is a real parameter. For which of the following sets of

c

-values does

p_c

attain its absolute maximum at

x=-2

? a)

c\ge 27

0<c<\dfrac{13}{4}

c\ge \dfrac{13}{4}

c\ge \dfrac{65}{8}