What is the maximum number of possible extreme values for the function,

f(x) = х2 + 4х2 – 3х – 18 ?

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 , where the quadratic term is positive, so the functions has a minimum at , where and , let's find that point