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Let f:[0,1]—> R be a thrice differentiable function such that f(0)= f (1) and f'(½)=f'(¾). Van f'''(x⁰) =0 for some x⁰=(0'1) Let f:[0,1]—> R be a thrice differentiable function such that f(0)= f (1) and f'(½)=f'(¾). Van f'''(x⁰) =0 for some x⁰=(0'1)
Dear StudentIf the function is cubic in between (0,1) and follows fiven condition then it is possible thatf'''(x⁰) =0 for some x⁰€(0,1)As the 2ndderivative of cubic function will be constantand derivative of constant function will be 0.Thanks
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