Let be a thrice differentiable function

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

Problem

Let

f:\mathbb{R}\to\mathbb{R}

be a thrice differentiable function. Suppose that

f(1)=0

f(3)=-4

, and

f'(x)<0

for all

x\in(1,3)

. The correct statement(s) is/are (1)

f'(1)<0

(2)

f(2)<0

(3)

f'(x)\ne0

for every

x\in(1,3)

(4)

f'(x)=0

for some

x\in(1,3)