For a twice-differentiable function

MATHEMATICS · Single correct · CBSE · Mathematics · Applications of Derivatives · Applications of Derivatives

Problem

f

, the second derivative satisfies

f''(x)>0

for

-5<x<-1

and for

x>3

f''(x)<0

for

-1<x<3

, and

f''(x)=0

only at

x=-1

and

x=3

. Which statement is true about the concavity of

f

and its points of inflection on the interval

(-5,6)

? (a)

f

is concave down on

(-5,-1)\cup(3,6)

and has points of inflection at

x=-1

and

x=3

. (b)

f

is concave up on

(-5,-1)\cup(3,6)

and has no points of inflection. (c)

f

is concave up on

(-5,-1)\cup(3,6)

and has points of inflection at

x=-1

and

x=3

. (d)

f

is concave up on

(-5,-1)\cup(3,6)

and has a point of inflection only at

x=-1