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 |

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

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(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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