JEE Main 2021MathematicsApplication of DerivativesEasyMCQ

JEE Main 2021 — Application of Derivatives Question with Solution

JEE Main 2021 (20 Jul Shift 1)

Question

Let a be a real number such that the function f(x)=ax2+6x-15,x∈R is increasing in -∞,34 and decreasing in 34,∞. Then the function g(x)=ax2-6x+15,x∈R has a

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Show full solutionCorrect option: A
Correct answer
Alocal maximum at x=-34

Step-by-step explanation

We have,

fx=ax2+6x-15

Graph of fx is shown below as it is increasing in -∞,34 and decreasing in 34,∞.

Then, abscissa of vertex is 34.

-B2A=34

⇒-(6)2a=34

⇒a=-4

∴g(x)=-4x2-6x+15

Local maxima exists at the vertex of gx, whose abscissa is

x=-B2A

⇒x=--6-8=-34

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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.