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Definite Integration question

2022 · 27 Jul · Shift 1 · Q38

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PYQ Library
JEE Main
Mathematics
Definite Integration
2022 · 27 Jul · Shift 1 · Q38

Definite Integration question

2022 · 27 Jul · Shift 1 · Q38

JEE MainMathematicsDefinite IntegrationMCQ+4 / −1

Let a function

f: \mathbb{R} \rightarrow \mathbb{R}

be defined as :

f(x)= \begin{cases}\int\limits_{0}^{x}(5-|t-3|) d t, & x\gt 4 \\ x^{2}+b x & , x \leq 4\end{cases}

where

\mathrm{b} \in \mathbb{R}

. If

f

is continuous at

x=4

, then which of the following statements is NOT true?

A
$f$ is not differentiable at $x=4$
B
$f^{\prime}(3)+f^{\prime}(5)=\frac{35}{4}$
C
$f$ is increasing in $\left(-\infty, \frac{1}{8}\right) \cup(8, \infty)$
D
$f$ has a local minima at $x=\frac{1}{8}$

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