Answer:
The function has at least 1 zero within the interval [-2,5].
Step-by-step explanation:
The intermediate value theorem states that, for a function continuous in a certain interval , then the function takes any value between
and
at some point within that interval.
This theorem has an important consequence:
If a function is continuous in an interval [a,b], and the sign of the function changes at the extreme points of the interval:
(or viceversa)
Then the function f(x) has at least one zero within the interval [a,b].
We can apply the theorem to this case. In fact, here we have a function f(x) continuous within the interval
[-2,5]
And we also know that the function changes sign at the extreme points of the interval:
Therefore, the function has at least 1 zero within the interval [-2,5], so there is at least one point x' within this interval such that