If f(x) = min {1, x2, x3}, then

f(x) = min. {1, x2, x3} ⇒ f(x) = ⇒ f(x) is continuous ∀ x ∈ R and non-differentiable at x = 1.

Math miscellaneousHard

Question

If f(x) = min {1, x², x³}, then

A.f(x) is continuous ∀ x ∈ R

B.f′(x) > 0,∀ x > 1

C.f(x) is not differentiable but continuous ∀ x ∈ R

D.f(x) is not differentiable for two values of x

f(x) = min. {1, x², x³}
⇒ f(x) =
⇒ f(x) is continuous ∀ x ∈ R
and non-differentiable at x = 1.

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