Quadratic Word Problem

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 the maximum amount of profit the company can make, to the nearest dollar. y=−9x^2+571x−3884

Answer 1

In order to find the maximum value of this graph, we have to find where the derivative is equal to zero. So, first, lets find the derivative of our function:

If f(x) = -9x^2+571x-3884, then f'(x) = -18x+571

Setting f'(x) equal to zero gives us: 0 = -18x+571

Now it's just a matter of solving for x! Once we do that, we see that x = 31.72

But remember, x is just the value for the number of widgets the company sells. In order to find the profit value that corresponds to that value of x, we have to plug x = 31.72 back into our original equation, f(x)

Doing that gives us our final value of y = $5173

Please let me know if you have any questions!