Question

Waterworks is a company that manufactures and sells paddle boards. It's profit P, in hundreds of dollars earned, is a function of the number of paddle boards sold x, measured in thousands. Profit is modeled by the function P(x)=-2x^3+34x^2-120x. What do the zeros of the function tell you about the number of paddle boards that waterworks should produce?

Answer 1

areAs given by the question

There are given that the profit function

$P(x)=-2x^3+34x^2-120x$

Now,

The zeros are the x values where the graph intersects the x axis.

Then,

To find the zeroes, replace P(x) with 0 and solve for x.

Then,

The zeroes of the given function is:

$\begin{gathered} P(x)=-2x^3+34x^2-120x \\ 0=-2x(x^2-17x^{}+60) \\ x^2-17x^{}+60=0 \\ (x-12)(x-5)=0 \\ x=0,\text{ 12, 5} \end{gathered}$

Hence, the zeroes of the function is 0, 12, 5.