Mathematics

Problem

For a twice-differentiable function

g

, selected values of

g''

are shown.

x

1

2

3

4

5

g''(x)

4

1

-1

-3

-2

Which statement is most strongly supported by the data? a)

g

changes concavity somewhere between

x=3

and

x=4

. b) The data are insufficient to determine whether

g

changes concavity on

1\le x\le5

. c)

g

changes concavity somewhere between

x=2

and

x=3

. d)

g

is concave up on

1\le x\le3

and concave down on

3\le x\le5