# Help with a problem?

##
the f be a function that is continuous on the closed interval [2,8]. Given that f(2)=2 and f(8)=12, which of the following statements is guaranteed by the intermediate value theorem

- f(x) is linear

2.f(x) is always increaseing

3.f(x)=7 has at least one solution in the open interval (2,8)

4.f(5)=7

5.there is at least one maximum on the open interval (2,8)

the f be a function that is continuous on the closed interval [2,8]. Given that f(2)=2 and f(8)=12, which of the following statements is guaranteed by the intermediate value theorem

- f(x) is linear

2.f(x) is always increaseing

3.f(x)=7 has at least one solution in the open interval (2,8)

4.f(5)=7

5.there is at least one maximum on the open interval (2,8)

##### 1 Answer

The third one.

#### Explanation:

The third one.

In fact as

As

On the contrary if you let:

the function is continuous for

If instead you let:

then the hypotheses are still satisfied but