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Question:

Let f:(-1, 1) → R be a function defined by f(x) = max{-|x|, -√(1 - x²)}. If K be the set of all points at which f is not differentiable, then K has exactly:

Two elements

Three elements

One element

Five elements

Solution:

f:(-1, 1) → R
f(x) = max{-|x|, -√(1 - x²)}
Non-derivable at 3 points in (-1, 1)