Let a function f: R → R be defined as: f(x)= ∫₀ˣ(5-|t-3|) d t, x>4 x²+b x, x ≤ 4 where b R. If f is continuous at x=4, then which of the following statements is NOT true?

(C) f is increasing in (-∞, 1/8) (8, ∞)

(A) f is not differentiable at x=4

(D) f has a local minima at x=1/8

Integral Calculus: JEE Main 2022 Mathematics question

JEE Main 2022 · 27 Jul, Morning shift · Q3441

JEE Main 202227 Jul, Morning shiftMathematicsMediumIntegral Calculus369× since 2002

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>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?

JEE Main 2022 Integral Calculus Question with Solution (27 Jul Morning shift, Q3441) | JEE Arc