Practicing Success

Target Exam

CUET

Subject

-- Mathematics - Section B1

Chapter

Determinants

Question:

Which of the following functions satisfies Rolle's theorem?

Options:

$f(x)=x, x \in[1,2]$

$f(x)=x^2, x \in[-1,1]$

$f(x)=x^3, x \in[-1,2]$

$f(x)=x^4, x \in[0,2]$

Correct Answer:

$f(x)=x^2, x \in[-1,1]$

Explanation:

for Rolle's theorem $f(a) = f(b)$ for f(x) defined in [a, b] 

for this case $f(x) = x^2 ,  x \in [-1, 1]$  as  $(-1)^2 = 1^2$