Define on the interval

MATHEMATICS · Single correct · A Level · Mathematics · Differentiation · Differentiation

Problem

Define

p_k(x)=e^{kx}\,(x^{2}-4x)

on the interval

(0,\infty)

, where

k

is a real parameter. For which values of

k

does

p_k

have exactly two relative extrema on

(0,\infty)

? (a)

k\le 0

(b)

k<0

k

(d)

k>0