Mathematics - Continuity - Differentiability Question with Solution | TestHub

MathematicsContinuity - DifferentiabilityContinuity- MiscellaneousMedium2 minPYQ_2021

MathematicsMediumsingle choice

Let $[t]$ denote the greatest integer less than or equal to $t .$
Let $f (x) = x - [x], g (x) = 1 - x + [x],$ and $h (x) = \min {f (x), g (x)}, x \in [- 2, 2] .$ Then $h$ is :

Options:

Answer:

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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