I really do not understand this it makes no sense, First off what is a dirative?

Question

I really do not understand this it makes no sense, First off what is a dirative? that is not discussed in my bookthat i can find and not been given in class? I do not understand how x2 - 40x becomes2x-40 ? what is dp and dx ? This section i really do not understand how or where it camefrom? I understand that x= 0 and y = -40 I mean i see how that wasobtained. not sure I understand this next part but somethingabout 0 and -40 are zeros so x + y divided by 2 gives -20 butif i try to put the -20 back in for eith x or y i still do not get20 can someone explain in plain terms how to walk thruthis?
dP/dx = 2x - 40

when at limit, dP/dx = 0
2x - 40 = 0
x - 20 = 0
x = 20

when x = 20,
y = x - 40
y = 20 - 40
y = -20

d²P/dx² = 2 > 0
since d²P/dx² is positive, P has a minimum value thanks, Jeff by the way does the chat feature on here work?
I really do not understand this it makes no sense, First off what is a dirative? that is not discussed in my bookthat i can find and not been given in class? I do not understand how x2 - 40x becomes2x-40 ? what is dp and dx ? This section i really do not understand how or where it camefrom? I understand that x= 0 and y = -40 I mean i see how that wasobtained. not sure I understand this next part but somethingabout 0 and -40 are zeros so x + y divided by 2 gives -20 butif i try to put the -20 back in for eith x or y i still do not get20 can someone explain in plain terms how to walk thruthis?
dP/dx = 2x - 40

when at limit, dP/dx = 0
2x - 40 = 0
x - 20 = 0
x = 20

when x = 20,
y = x - 40
y = 20 - 40
y = -20

d²P/dx² = 2 > 0
since d²P/dx² is positive, P has a minimum value thanks, Jeff by the way does the chat feature on here work?

Explanation / Answer

First a derivative means the rate of change, for : dp/dxit simply means the change of the function p with restect to x. Soyour function p has to equal to some value of x. lets say p=x2 then : dp/dx= 2x   ( Whenyou take a derivative of a function, in this example x2,the power of the function becomes the coefficient, x2derived becomes 2x, you just bring the two down. Lets say p= x3 then dp/dx= 3x2 (the power three became the coefficient, and whaterver the powerwas the new power for x will be the old power minus 1, in thisexample: 3-1=2, that why the power of x is two in thederivative. This true for the first example also, the power was 2 so forthe derivative 2-1=1, thats why you only have 2x. It is true for all derivatives. other examples:  p= x 4 so dp/dx= 4x3    (4-1=3)                           p=2x5 so dp/dx= 2*5x4= 10x4                          p=x so dp/dx = 1 (because the power of x is 1 so 1-1=0,and anything to the 0 is equal to 1) Now to take your example:   p=x2-40x   then dp/dx= 2x-40 (you do thederivative of each element separatly, x2 and 40x) Hope this helps if you have more questions feel free toask.                          p=x so dp/dx = 1 (because the power of x is 1 so 1-1=0,and anything to the 0 is equal to 1) Now to take your example:   p=x2-40x   then dp/dx= 2x-40 (you do thederivative of each element separatly, x2 and 40x) Hope this helps if you have more questions feel free toask.

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