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Let  be a non-constant thrice differentiable function defined on  such that  and . If  is the minimum number or roots of  in the interval [0, 6], then the value of  is



Question ID - 153400 | SaraNextGen Top Answer

Let  be a non-constant thrice differentiable function defined on  such that  and . If  is the minimum number or roots of  in the interval [0, 6], then the value of  is

1 Answer
127 votes
Answer Key / Explanation : (6) -

(6)

     (1)

On differentiating (1) w.r.t. , we get

        (2)

Putting  in (2), we get

Similarly

has minimum 7 roots in [0, 6]

Now, consider a function

As  satisfy Rolle’s theorem in intervals  and  respectively

So, by Rolle’s theorem, the equation  has minimum 6 roots

Now , where

Clearly  has minimum 13 roots in [0, 6]

Hence again by Rolle’s theorem, has minimum 12 zeroes in [0, 6]

127 votes


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