JEE Main 2021MathematicsApplication of DerivativesHardMCQ

JEE Main 2021 — Application of Derivatives Question with Solution

JEE Main 2021 (24 Feb Shift 2)

Question

Let f:R→R be defined as

fx=-55x,if x<-52x3-3x2-120x,if-5≤x≤42x3-3x2-36x-336,if x>4

Let A={x∈R:f is increasing}. Then A is equal to:

Choose an option

Show full solutionCorrect option: B
Correct answer
B-5, -4∪4, ∞

Step-by-step explanation

fx=-55x,if x<-52x3-3x2-120x,if-5≤x≤42x3-3x2-36x-336,if x>4

f'x=-55,if x<-56x2-6x-120,if-5≤x≤46x2-6x-36,if x>4

f'x=-55;x<-56x-5x+4;-5<x<46x-3x+2;x>4

fx is increasing

⇒f'x>0

So, x∈-5,-4∪4,∞

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About this question

This is a previous-year question from JEE Main 2021, covering the Application of Derivatives chapter of Mathematics. PrepSharp catalogues every PYQ from JEE Main with a verified answer key and step-by-step solution prepared by IIT alumni — so you can search by chapter, topic or year and revise efficiently.