Question

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

(1) h is not continuous 

(2) h is differentiable for all x 

(3) h′(x) = 0 for all x > 1 

(4) h is not differentiable at two values of x 

Answer 1

Correct Option(4) h is not differentiable at two values of x

Explanation:

h(x) = min {x, x² } for all x implies

h(x) is continuous at 0 and 1 and hence for all x.

h(x) is not differentiable at x = 0 and at x = 1

h′ (0 − ) = 1 and h′(0 + ) = 0 

h′ (1 − ) = 2 and h′(1 + ) = 1 

Also h′(x) = 1 for all x > 1