00:01
In this question, we are told that the profit from selling calculus textbooks is given by the function p.
00:07
And we are asked to find the additional profit when the sales increase from 150 to 151 books.
00:15
And we are asked to find the marginal profit when x equals to 150.
00:22
To find the additional profit, we simply need to calculate p of 151 minus p of 150.
00:29
The profit we get from selling 151 books minus the profit from selling 150 books.
00:40
So, p of 151 is going to be negative 0 .05 times 151 squared plus 20 times 151, minus 1000, minus p of 150 equals to negative 0 .05 times 150 squared plus 20 times 150 minus 1000.
01:09
Now we need to simplify that expression.
01:11
First of all, note that we can cancel 1000.
01:16
Next, what we can do is we can combine 151 squared and 150 squared by factoring out 0 .05, negative 0 .05.
01:30
We are going to get 151 squared minus 150 squared in parentheses and we can also combine 151 and 150 by factoring out 20.
01:49
So this is what we are going to get.
01:51
Now we need to calculate 151 squared minus 150 squared and that's going to be 301 and plus 20, right? because 151 minus 150 equals to 1.
02:07
All right, now 301 times 0 .05 equals to 15 .05 plus 20 so that's going to be 35 .05.
02:33
Sorry, i forgot the negative sign.
02:40
So there is a negative sign in front.
02:45
And so it's 20 minus 15 .05 and that's going to be 4 .95...