JEE Advanced2006MathematicsContinuity and DifferentiabilityActual

If f(x)= 1, x^2, x^3 , then

Options

Af(x) is continuous everywhere
Bf(x) is continuous and differentiable everywhere
Cf(x) is not differentiable at two points
Df(x) is not differentiable at one point

Correct answer

A. f(x) is continuous everywhere

Step-by-step solution

Here, f(x)= . 1, x^2, x^3 which could be graphically shown as f(x)= array c 1, x 1 x^3, x f(x) is continuous for x R and not differentiable at x=1 due to sharp edge.

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