Question

If f (x) = min {1, x², x³ } then

(a) f(x) is continuous everywhere

(b) f(x) is continuous and differentiable everywhere

(c) f(x) is not differentiable at two points

(d) f(x) is not differentiable at one point

Answer 1

Correct option 

(a) f(x) is continuous everywhere

(d) f(x) is not differentiable at one point

Explanation :

Here, f (x) = min {1, x², x³ } which could be graphically shown as

f(x) is continuous for x ∈ R and not differentiable at

x = 1 due to sharp edge.