Question

Let f (x) = min { x, $x^2$ } for every real number of x, then

• A. h is continuous for all x
• B. h is differentiable for all x
• C. h ' (x) = 1, $\forall$ x > 1
• D. h is not differentiable at two values of x

Answer 1

Answer: (A), (C), (D)

From the figure,
h (x) is continuous all x, but hix) is not differentiable at
two points x = 0 and x = l . (due to sharp edges). Also
h ' (x) = 1, $\forall$ x > 1
Hence, (a), (c) and (d) is correct answers,