Question

If f (x) = min { 1, $x^2, x^3$ }, 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

Answer: (D)

f (x) is not differentiable at one point

Answer 2

The correct option are(A and D): f (x) is continuous everywhere and f (x) is not differentiable at one point.

Here, f (x) = min { 1, $x^2, x^3$ } which could be graphically
shown as
$\Rightarrow$ f (x) is continuous for x $\in$ R and not differentiable at
x = 1 due to sharp edge.
Hence, (a) and (d) are correct answers.