# Flett's Theorem

Flett's Theorem

Flett's theorem: Given a function differentiable on with , there is an intermediate point such that

f(x)

[a,b]

f'(a)=f'(b)

c

f'(c)=

f(c)-f(a)

c-a

Geometric interpretation: The secant line connecting the points and is exactly the tangent line to the curve at the point .

(a,f(a))

(c,f(c))

y=f(x)

(c,f(c))

The example used is the function on the interval .

f(x)=+x+

a

0

a

1

a

3

3

x

[-a,a]