Question 995708
to find out the point where profit is equal to 0, just set the equation equal to 0 and solve.


you get:


-4x^3 + 12x^2 + 16x = 0


factor out the gcf to get:


(-4x) * (x^2 - 3x - 4) = 0


factor x^2 - 3x - 4 to get:


(-4x) * (x-4) * (x+1) = 0


set each of these factors equal to 0 and solve for x to get:


x = 0, x = 4, x = -1.


x represents number of tablets.


x = 0 leads to a profit of 0 but that's trivial.
x = -1 is invalid because number of tablets can't be negative.
only valid answer is that profit is 0 when x = 4.


you have 3 zero crossing points and you want to see whether profit is positive or negative between them.


the only intervals that are valid are the intervals between x = 0 and x = 4, and the interval where x is greater than 4.


it turns out that x is positive in the interval between x = 0 and x = 4 only.


it is negative otherwise.


if you look at the graph, you will see that the same profit is made when x = 2 and when x = 3.


that can be seen by drawing a horizontal line at y = 48 and the intersection will be at x = 2 and x = 3.


the grpah of your equation is shown below along with the line of y = 48.


results on the graph are in millions.


when x = 2 million, you make a 48 million profit.
when x = 3 million, you make a 48 million profit.



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