WOLFRAM NOTEBOOK

Bolzano's Theorem

1.5

4.5

Bolzano's theorem states that if

is a continuous function in the closed interval

[a,b]

with

f(a)

and

f(b)

of opposite sign, then there is a

in the open interval

(a,b)

such that

f(c)=0

Snapshot 1: The function is positive in the interval and therefore

f(x)>0

for all

(a,b)

Snapshot 2: The function is negative in the interval so

f(x)<0

for all

(a,b)

Snapshot 3: The function is positive for

f(a)

and negative for

f(b)

, therefore there is a

(a,b)

such that

f(c)=0

Julio Cesar de la Yncera

You are using a browser not supported by the Wolfram Cloud

Supported browsers include recent versions of Chrome, Edge, Firefox and Safari.

I understand and wish to continue anyway »