00:02
So in this question, we're told basically that an appliance manufacturer finds that if they sell x blenders annually, the total profit in dollars is given by the following p of x is 8x plus 0 .3x squared minus 0 .013x cubed minus 371.
00:27
And we're told in part a to graph the function on an appropriate window.
00:37
So i'll do this and it looks something like this.
00:44
So here's your p of x.
00:49
Maybe this is 3000.
00:53
We don't really care about what happens for negative x values because it doesn't make sense physically to produce negative blenders.
00:59
So really only they care about the part where x is positive.
01:03
So you can see there's two points where we cross the x axis, which correspond to zero profit.
01:12
So for some amount of the time, right in this green part, but i just highlighted, they're actually losing money.
01:19
They're making a negative profit.
01:23
And really what we want to figure out in part a is how many blenders must be produced, break -even.
01:34
So we exactly want to find the x intercepts of this.
01:39
And so you know, you set p of x equal to zero and solve.
01:46
So if you're using your calculator, or you're looking at the graph, the first value happens at 25 .1851.
02:02
And then that second value happens at about 250 .771...