Functions and are continuous on and differentiable on

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

Problem

Functions

h

and

p

are continuous on

[a,b]

and differentiable on

(a,b)

. Suppose

h'(x) > p'(x)

for every

x

(a,b)

. Which statement is necessarily true? (a)

h

and

p

intersect at least twice on

(a,b)

. (b)

h(x)-p(x)

has a critical point in

(a,b)

. (c) If

h(a)=p(a)

, then

h(x)>p(x)

for all

x\in (a,b]

. (d) There exists

c\in(a,b)

such that

h'(c)=p'(c)