Respuesta :
Answer:
(0.3, -18.45).
Step-by-step explanation:
We need to recur to the extreme value theorem, which states: "If a function is continuous on a closed interval, then that function has a maximum and a minimum inside that interval".
Basically, as the theorem states, if a dunction is continuous, then it has maxium or minium.
In this case, we have a quadratic function, which is a parabola. An important characteristic of parabolas is that they have a maximum or a minium, but they don't have both. When the quadratic term of the fuction is positive, then it has a minium at its vertex. When the quadratic term of the function is negative, then it has a maximum at its vertex.
So, the given function is [tex]f(x)=x^{2} +4x^{2} -3x-18=5x^{2} -3x-18[/tex], where the quadratic term is positive, so the functions has a minimum at [tex]V(h,k)[/tex], where [tex]h=-\frac{b}{2a}[/tex] and [tex]k=f(h)[/tex], let's find that point
