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Please solve this question Statement 1: if f(x) = e^[(x-1)(x-3)], then rolle theorem is applicable to f(x) in the interval [1,3]. Statement 2: mean value theorem is applicable to the above mentioned function in the interval [1,4]. Say whether statement 1 and 2 are correct ? And whether statement 2 is the correct explanation for statement 1?? Please explain in detail.

Please solve this question
Statement 1: if f(x) = e^[(x-1)(x-3)], then rolle theorem is applicable to f(x) in the interval [1,3].
Statement 2: mean value theorem is applicable to the above mentioned function in the interval [1,4].
Say whether statement 1 and 2 are correct ?
And whether statement 2 is the correct explanation for statement 1??
Please explain in detail.

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1 Answers

Aditya Gupta
2081 Points
3 years ago
both statements are true. but statement 2 is not the correct explanation for statement 1.
we see that f(1)=f(3), and that it is differentiable, so obviously rolle theorem is applicable to f(x) in the interval [1,3].
MVT is applicable in any interval [a,b], as long as the function is differentiable in that interval. since f(x) given above is differentiable in R, so statement 2 is true as well.
obviously though it does not explain st1 in any way

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