Question

The volume, in cubic centimeters, of a fish tank is represented by the polynomial model V(x)=36x^2-3.75x^3. Is the polynomials maximum value relative or absolute?A. RelativeB. Absolute

Answer 1

Snake, this is the solution to the problem:

Let's recall the definition of relative maximum and absolute values:

Relative maximum value: This is a point where the function changes direction from increasing to decreasing (making that point a "peak" in the graph).

On the other hand, relative minimum value is th point where the function changes direction from decreasing to increasing (making that point a "bottom" in the graph).

Now we can define that an absolute maximum point is a point where the function obtains its greatest possible value.

Using the derivative, we can calculate the maxim value:

(32/5, 12,288/25)

In consequence, this polynomial is at:

A. Relative maximum value.