Question

Let f:[0,1] → R be a thrice differentiable function such that f(0) = f(1) and [1]
f
′
(
1
2
) = f′ (
3
4
) . Can f
′′′(x0
) = 0 for some x0 ∈ (0,1) ?

Give brief explanation.

Answer 1

Answer:

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Answer 2

• 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.