# How do you verify the intermediate value theorem over the interval [0,3], and find the c that is guaranteed by the theorem such that f(c)=0 where #f(x)=x^2-6x+8#?

##### 1 Answer

Intermediate Value theorem is verified so, there exist

such that

#### Explanation:

Intermediate Value theorem is defined over

Because

then there exist

Factorization in the previous step is determined by applying :

Factorization here is determined by applying the followingbidentiyy:

Or