# How do you use the intermediate value theorem to explain why #f(x)=x^2-x-cosx# has a zero in the interval [0,pi]?

##### 1 Answer

Jan 8, 2017

See explanation...

#### Explanation:

The intermediate value theorem tells us that if

In our example:

#f(x) = x^2-x-cos x#

#f(x)# is continuous on#[0, pi]# (in fact on the whole of#RR# )

#f(0) = 0-0-cos(0) = -1 < 0#

#f(pi) = pi^2-pi-cos(pi) = pi(pi-1)+1 > 3(3-1)+1 = 7 > 0#

So