MathDB

Let

f:\mathbb{R} \to \mathbb{R}

be a function that is a function that is differentiable

n+1

times for some positive integer

n

. The

i^{th}

derivative of

f

is denoted by

f^{(i)}

. Suppose-

f(1)=f(0)=f^{(1)}(0)=...=f^{(n)}(0)=0

.
Prove that

f^{(n+1)}(x)=0

for some

x \in (0,1)

Problem Statement