Continuity and DifferentiabilityHard

Question

Let h(x) = min {x, x2} for every real number of x, then

Options

A.h is differentiable for all x
B.h is continuous for all x
C.h′(x) = 1, for all x > 1
D.h is not differentiable at two values of x,

Solution

      
From the figure.
h(x) is continuous all x, but h(x) is not differentiable at two points x = 0 and x = 1 (due to sharp edges). Also h′(x) = 1, ∀ x > 1
Hence (b),(c) and (d) is correct answers.

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