Question

Imagine the polynomial function shown represents the profits, in y dollars, earned by the production of x widgets.

What is the minimum number of widgets for the company to earn more than 50 dollars?

widgets

Answer 1

I don't have the graph or the polynomial — could you either attach the picture or type the polynomial rule (or list the x-values where the curve crosses y = 50)?

How I'll solve it once you provide that:
1. Let f(x) be the polynomial. Solve f(x) = 50 (equivalently f(x) − 50 = 0) to find the boundary x-values.
2. Use those roots and a sign chart (or test points) to find the x-interval(s) where f(x) > 50.
3. The minimum number of widgets is the smallest x in that interval. If you must produce an integer number of widgets, take the smallest integer x for which f(x) > 50: that is, the smallest integer greater than or equal to the left endpoint of the interval, except if the left endpoint is a root (f = 50) you must take the next integer.

Send the graph or the polynomial (or the intersection points with y = 50) and I’ll compute the exact number.