TIFR-2015-Maths-A-5

Question

Let $f : \mathbb{R} \rightarrow \mathbb{R}$ denote the function defined by $f(x)= (1-x^{2})^{\frac{3}{2}}$ if $|x| < 1$, and $f(x)=0$ if $|x| \geq 1$. Which of the following statements is correct ?

• A. $f$ is not continuous
• B. $f$ is continuous but not differentiable
• C. $f$ is differentiable but $f'$ is not continuous.
• D. $f$ is differentiable and $f'$ is continuous.

Answer 1

F(x) is continuous at -1 and 1.
Ans 4

Comments

explain more why option 4 is correct and rest are not.