For a function that is continuous on and differentiable on with for every in

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

Problem

For a function

f

that is continuous on

[1,4]

and differentiable on

(1,4)

with

f'(x)>0

for every

x

(1,4)

, which statement must be true? (a)

f(1)=f(4)

(b)

f''(x)>0

for every

x

(1,4)

(c)

f

is increasing on

[1,4]

(d) There exists

c

(1,4)

such that

f'(c)=0