JEE Main 2020MathematicsDifferentiationMediumMCQ

JEE Main 2020 — Differentiation Question with Solution

JEE Main 2020 (09 Jan Shift 1)

Question

Let f be any function continuous on a,b and twice differentiable on a,b . If all x∈a,b,f'x>0 and f''x<0 , then for any c∈a,b,fc-fafb-fc

Choose an option

Show full solutionCorrect option: D
Correct answer
Dc-ab-c

Step-by-step explanation

Let’s use LMVT for x∈a,c

fc-f(a)c-a=f'α,α∈a,c

Also use LMVT for x∈c,b

fb-f(c)b-c=f'β,β∈c,b

∵f''x<0⇒f'x is decreasing

f'α>f'β

fc-f(a)c-a>fb-f(c)b-c

fc-f(a)fb-f(c)>c-ab-c ( ∵f(x) is increasing)

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About this question

This is a previous-year question from JEE Main 2020, covering the Differentiation 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.