The derivative of a differentiable function has exactly two -intercepts at and

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

Problem

The derivative

h'

of a differentiable function

h

has exactly two

x

-intercepts at

x=-3

and

x=1

. The graph of

h'

is positive on

(-3,1)

and negative on

(-\infty,-3)

and

(1,\infty)

. Which of the following best describes the corresponding behavior of

h

? (a)

h

has a local maximum at

x=-3

and a local minimum at

x=1

. (b)

h

has a local minimum at

x=-3

and a local maximum at

x=1

. (c)

h

is decreasing on

(-3,1)

and increasing on

(-\infty,-3)\cup(1,\infty)

. (d)

h

is concave up on

(-3,1)

and concave down elsewhere.