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  4. Consider the function f(x)=min |x2 - 4| , |x2 - 1| , then the number of points where f(x) is non-differentiable is/are

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Q. Consider the function $f\left(x\right)=min \left\{\left|x^{2} - 4\right| , \left|x^{2} - 1\right|\right\}$ , then the number of points where $f\left(x\right)$ is non-differentiable is/are

NTA AbhyasNTA Abhyas 2020Continuity and Differentiability

Solution:

Using the graph of $y=\left|x^{2} - 4\right|,y=\left|x^{2} - 1\right|$
Solution
Clearly, from the graph we can see $f\left(x\right)$ is non-differentiable at $6$ points.