Let F be thrice differentiable... | JEE Advanced | Functions

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JEE Advance 2015

Paper-2 2015

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Question

Let $F: R \rightarrow R$ be a thrice differentiable function. Supose that $F(1)=0, F(3)=-4$ and $F^{\prime}(x)<0$ for all $x \in(1 / 2,3)$. Let $f(x)=x F(x)$ for all $x \in R$. The correct statement(s) is(are):

Select ALL correct options:

A

$f^{\prime}(1)<0$

B

$f(2)<0$

C

$f^{\prime}(x) \neq 0$ for any $x \in(1,3)$

D

$f^{\prime}(x)=0$ for some $x \in(1,3)$

✓ Correct! Well done.

✗ Incorrect. Try again or view the solution.

⚠ Partially correct. Some answers are missing.

Solution

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