00:01
So the marginal profit function, m, is just equal to the derivative of our profit function, so p prime.
00:08
The rule, or the derivative rule that we're going to use to figure out this derivative is the power rule.
00:14
So the power rule is, if we have a derivative of x raises some power n, and that's just equal to n times x to the n minus one power.
00:24
So we're going to use that to figure out this derivative later as well as other properties of derivatives.
00:29
So we know the derivative, or m is equal to the derivative of our profit function.
00:35
So m is going to be equal to the derivative of negative 2x squared plus 72x minus 145.
00:48
And whenever we have a derivative of a term plus or minus another term, it's equal to the derivative of the first term plus the derivative of the second term.
00:57
So we can split this derivative up.
00:59
So we can say m is equal to the derivative negative 2x squared, plus the derivative of 72x, and then minus the derivative of 145.
01:20
So we know that derivatives of constants go to zero.
01:23
So this derivative of 145, that's just going to be equal to zero.
01:26
So we can simplify this...