JEE Main 2022MathematicsContinuity and DifferentiabilityHardNumerical

JEE Main 2022 — Continuity and Differentiability Question with Solution

JEE Main 2022 (25 Jul Shift 1)

Question

Let fx=4x2-8x+5,if 8x2-6x+1≥04x2-8x+5,if 8x2-6x+1<0, where α denotes the greatest integer less than or equal to α. Then the number of points in R where f is not differentiable is _____ .

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Show full solutionCorrect answer: 3
Correct answer
3

Step-by-step explanation

Given,

fx=4x2-8x+5,if 8x2-6x+1≥04x2-8x+5,if 8x2-6x+1<0

=4x2-8x+5,if x∈−∞,14∪12,∞4x2-8x+5if x∈14,12

⇒fx=4x2−8x+5if x∈−∞,14∪12,∞3x∈14,2−222x∈2−22,12

Now plotting the graph of fx we get,

We can see fx is not differentiable at 14,x1,12 (wherex1=2-22)

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About this question

This is a previous-year question from JEE Main 2022, covering the Continuity and Differentiability 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.