Mathematics

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.