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Question

According to Rolle’s theorem, there will be at least one solution for f’(x) = 0 in the interval [-2,2], where f(x)=1x2


A

True

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B

False

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Solution

The correct option is B

False


Rolle’s theorem states that if we have a function which is continuous in [a,b] , differentiable in (a, b) and f(a) = f(b), then there is at least one c , between a to b such that f’(c) = 0. Here, the value of the function at x = 2 and x = -2 are equal (=122). So, can we say Rolle’s theorem is applicable here and there should be at least one solution for f’(x) = 0?

We should also check if the function is continuous in the given interval. As we can see from the graph of 1x2, it is discontinuous at x = 0. So, we can’t apply Rolle’s theorem here.

In fact f(x)=2x3 has no solution in the interval [-2,2]


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