Let a function f: \mathbb{R} \to \mathbb{R} be defined as : f(x)=\\begin{array}{c}\int_{0\end{array}^{x}(5-{|t-3|}) d t, {, } x>4 ; x^2+b x {, } , x \leq 4 where {\b} \in \mathbb{R}. If f is continuous at x=4, then which of the following statements is NOT true? [27-Jul-2022-Shift-1]

Correct Answer is : f is increasing in (−∞,18)∪(8,∞)

f is increasing in (-\infty, \frac{1}{8}) \cup(8, \infty)

f has a local minima at x=\frac{1}{8}

JEE Mains 27-July-2022 Shift 1 Solved Paper

Section: Mathematics

Question : 20 of 90

Marks: +1, -0

Let a function f:ℝ→ℝ be defined as :
f(x)={

∫

(5−|t−3|)dt

,‌x>4

x2+bx,‌

x≤4

where b∈ℝ. If f is continuous at x=4, then which of the following statements is NOT true?

[27-Jul-2022-Shift-1]

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