Let and define for all real

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

Problem

Let

k>0

and define

f_k(x)=e^{kx}-x

for all real

x

. Which of the following is always true for every such

k

? (a)

f_k

possesses exactly one local maximum and no local minimum. (b)

f_k

possesses exactly one local minimum and no local maximum. (c)

f_k

possesses one local minimum and one local maximum. (d)

f_k

possesses no local extremum.