MathDB

Suppose that

f:[0,1]\to\mathbb R

is a continuously differentiable function such that

f(0)=f(1)=0

and

f(a)=\sqrt3

for some

a\in(0,1)

. Prove that there exist two tangents to the graph of

f

that form an equilateral triangle with an appropriate segment of the

x

-axis.

Problem Statement