Let f (x) = min x, x2 for every real number of x, then

Question

Let f (x) = min x, x2 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, ∀ x > 1 (D) h is not differentiable at two values of x

Tardigrade Admin · Accepted Answer

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, ∀ x > 1 Hence, (a), (c) and (d) is correct answers,

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

h is continuous for all x

h is differentiable for all x

h ' (x) = 1, $\forall$ x > 1

h is not differentiable at two values of x

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,

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