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Mathematics - Continuity - Differentiability Question with Solution | TestHub

MathematicsContinuity - DifferentiabilityContinuity- MiscellaneousMedium2 minPYQ_2021
MathematicsMediumsingle choice

Let[t]denote the greatest integer less than or equal tot.
Letf(x)=x-[x], g(x)=1-x+[x],andh(x)=min{f(x),g(x)},x[-2,2].Thenhis :

Question diagram: Let [ t ] denote the greatest integer less than or equal to

Options:

Answer:
A
Solution:

f(x)=x-[x]={x}

g(x)=1-x+[x]=1-{x}

Now, Graph of min {f(x),g(x)}

Clearly graph is continuous in [-2,2] but non differentiable at 7 points (i.e. greater than 4) in (-2,2)

Stream:JEESubject:MathematicsTopic:Continuity - DifferentiabilitySubtopic:Continuity- Miscellaneous
2mℹ️ Source: PYQ_2021

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