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)

Question

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)

Harshit Singh · Answer

Dear Student

If the function is cubic in between (0,1) and follows fiven condition then it is possible that

f'''(x⁰) =0 for some x⁰€(0,1)
As the 2ndderivative of cubic function will be constant
and derivative of constant function will be 0.
Thanks

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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)

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