If rolle-s theorem is applicable onfx-x-x-12 in -0-1- then the value of - can be

Given : f(x)=x^α(x 1)^2 clearly, f(x) will become discontinuous at x=0, if α lt;0. For α≥ 0 : f(x) is continuous and differentiable in given interval. but f( ...

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Standard XII

Mathematics

Implicit Differentiation

If rolle's th...

Question

If rolle's theorem is applicable on $f (x) = x^{α} (x - 1)^{2}$ in $[0, 1],$ then the value of $α$ can be

- 1

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2

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0

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\frac{1}{3}

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Solution

The correct option is D $\frac{1}{3}$
Given : $f (x) = x^{α} (x - 1)^{2}$
clearly, $f (x)$ will become discontinuous at $x = 0,$ if $α < 0.$

For $α \geq 0 : f (x)$ is continuous and differentiable in given interval.
but $f (0)$ is not defined for $α = 0$

So, only possible values for which $f (0) = f (1) = 0$ are $α > 0$

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If rolle's theorem is applicable onf(x)=xα(x−1)2 in [0,1], then the value of α can be

The correct option is D 13Given : f(x)=xα(x−1)2 clearly, f(x) will become discontinuous at x=0, if α<0. For α≥0:f(x) is continuous and differentiable in given interval. but f(0) is not defined for α=0 So, only possible values for which f(0)=f(1)=0 are α>0

If rolle's theorem is applicable on $f (x) = x^{α} (x - 1)^{2}$ in $[0, 1],$ then the value of $α$ can be