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Question
If f(x) = `{{:(x^2"," if x ≥ 1),(x"," if x < 1):}`, then show that f is not differentiable at x = 1.
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Solution
∵ f(x) = `{{:(x^2"," if x ≥ 1),(x"," if x < 1):}`
then f'(x) = `{{:(2x"," if x ≥ 1),(1"," if x < 1):}`
LHD of f(x) = 1
RHD of f(x) = 2x = 2
Since LHD ≠ RHD
It is not differentiable at x = 1.
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