A function is continuous on and satisfies the following

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

Problem

A function

f

is continuous on

(0,6)

and satisfies the following. •

f

is increasing on

(0,3)

and decreasing on

(3,6)

. •

f

has a local maximum at

x=3

. Let

F(x)=\displaystyle\int_{1}^{x} f(t)\,dt

for

1\le x\le6

. Which statement about the concavity of

F

is true? (a)

F

is concave up on

(0,3)

and concave up on

(3,6)

. (b)

F

is concave down on

(0,3)

and concave up on

(3,6)

. (c)

F

is concave up on

(0,3)

and concave down on

(3,6)

. (d)

F

is concave down on both

(0,3)

and

(3,6)