Intermediate Value Theorem

slope

0.5

intercept

0.34

move c

0.32

show interval labels

If

f

is continuous on a closed interval

[a,b]

, and

c

is any number in the closed interval between

f(a)

and

f(b)

, then there is at least one number

x

in

[a,b]

such that

f(x)=c

.

External Links

Intermediate Value Theorem (Wolfram MathWorld)

Bolzano's Theorem

Permanent Citation

Izidor Hafner

"Intermediate Value Theorem"
http://demonstrations.wolfram.com/IntermediateValueTheorem/
Wolfram Demonstrations Project
Published: March 7, 2011