Let f:[0,1] —>R be a thrice differentiable function such that f(0)=f(1) and f'(½)=f'(¾) can f'''(x⁰) =0 for some x⁰€(0,1)

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 2^ndderivative of cubic function will be constant
and derivative of constant function will be 0.
Thanks