Question

A company sells widgets. The amount of profit, y, made by the company, is related to

the selling price of each widget, x, by the given equation. Using this equation, find out
what price the widgets should be sold for, to the nearest cent, for the company to
make the maximum profit.
y=-9x² + 700x - 6005

Answer 1

$38.89.

Explanation:

In this problem we have a quadratic equation, which, as you may already know, consists on a curve that has a maximum or minimum value, depending whether the x^2 value has a positive of negative sign before it.

In this case, the equation has a negative sign, which indicates that his function has a maximum point, which is the same point we are looking for in order to get the price widgets should be sold for, for the company to make the maximum profit. Now that we know that, let's go ahead and find the maximum value of the function. I'm gonna solve this on a digital board and attatch the images to this answer.

If you don't feel familiar with the process of taking derivatives, I suggest you watch some videos of explanations of this topic. Also, you can use Ron Larsson's Calculus books to practice derivation. Good luck!