A twice-differentiable function has first derivative

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

Problem

A twice-differentiable function

h

has first derivative

h'(x)=x^{2}e^{-x}(x-3)

. Which of the following statements about the graph of

h

is true? (a)

h

has a local maximum at

x=0

and a local minimum at

x=3

. (b)

h

has a local minimum at

x=0

and a local maximum at

x=3

. (c)

h

has neither a local maximum nor a local minimum at

x=0

, and it has a local minimum at

x=3

. (d)

h

has local minima at both

x=0

and

x=3