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 |
(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] |