Mathematics

Problem

Curves J, K, and L have the following observed properties. • J has critical points at

x=-1

and

x=3

. It is decreasing on

(-\infty,-1)

, increasing on

(-1,3)

, and decreasing on

(3,\infty)

. • K crosses the

x

-axis at

x=-1

and

x=3

and is positive on

(-1,3)

while negative on the intervals

(-\infty,-1)

and

(3,\infty)

. • L crosses the

x

-axis only at

x=1

; it is positive for

x<1

and negative for

x>1

. Assuming exactly one of the three curves is a twice-differentiable function

f

and the other two are its derivatives, which identification is most consistent with these observations? a) J is

f'

, K is

f''

, L is

f

b) J is

f''

, K is

f

, L is

f'

c) J is

f

, K is

f'

, L is

f''

d) J is

f

, L is

f'

, K is

f''