Let be a differentiable function whose first derivative is increasing for

MATHEMATICS · Single correct · AP · Calculus AB · Analytical Applications of Differentiation · Analytical Applications of Differentiation

Problem

Let

g

be a differentiable function whose first derivative

g'(x)

is increasing for

-2<x<1

, attains a maximum at

x=1

, and is decreasing for

1<x<4

. Which of the following must be true about

g''

x=1

? (a)

g''(1)=0

and changes sign from positive to negative at

x=1

. (b)

g''(1)=0

and changes sign from negative to positive at

x=1

. (c)

g''(1)>0

. (d)

g''(1)<0