GO Classes Test Series 2023 | Calculus | Test 1 | Question: 5

Answer 1

$f(x)=1-x^{2 / 3}\Rightarrow$  not differentiable at $0.$

$g(x)=x^{3}-2 x^{2}-x+2 \Rightarrow g(-1) = g(1)$

$h(x)=\cos \left(\frac{\pi}{4}(x+1)\right)\Rightarrow  h(-1) \neq h(1)$

Answer 2

Rolle’s Theorem states that,

The function f(x) must be continuous in [-1,1], differentiable in (-1,1). and f(-1) = f(1)

F(x) isn’t differentiable at x=0, as f’x = -2/3 x^-1/3 , so f(x) doesn’t satisfy rolle’s theorem.

G(x) satisfy all conditions

H(x) doesn’t satisfy f(-1) = f(1)