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 [tex][a,b][/tex], then the function takes any value between [tex]f(a)[/tex] and [tex]f(b)[/tex] at some point within that interval.
This theorem has an important consequence:
If a function [tex]f(x)[/tex] is continuous in an interval [a,b], and the sign of the function changes at the extreme points of the interval:
[tex]f(a)>0\\f(b)<0[/tex] (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:
[tex]f(-2)=-7<0\\f(5)=1>0[/tex]
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
[tex]f(x')=0[/tex]
