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]