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help me with optimization for calculus

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a computer company determines its profit equation in millions of dollars given by p=x^3-48x^2+720x-1000 where x is the number of thousands of units of software sold
and 0
im thinking this is really ez.... but maybe im wrong.... since from 0-40 it looks like a line almost.... wouldnt (40,y) b the maximum?

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or maybe im wrong
|dw:1355889094401:dw|It's a cubic function, so it's going to have this shape. As I've illustrated in the picture, it is possible that 40 might not be the maximum profit value. So we'll have to do some work to find out where that point is.
do i differentiate the function and find the critical values?
\[\large P(x)=x^3-48x^2+720x-1000\]Yes very good. You'll want to find Critical Points, and since this is a CLOSED INTERVAL, also check the END POINTS! Then simply plug each value into the function, and see which gives you the largest output.
oh if thats how it looked then i graphed it wrong.. my bad
Hmm I better throw it into wolfram and make sure I'm not way off.. cause I was just doing that based off of memory :P
but anyways it be best to just find derivative.. and critical points.. then find values of those and the 0/40 and then u get ur answer
would my critical values be x<12, 1220?
ur critical valued would be points.....
You got the correct points, x=12, x=20. I'm not sure why you wrote them as intervals though :)
Now you want to plug your values into P(x) and compare, to find out which one gives you the largest value within this closed interval.\[\large P(12),\quad P(20), \quad P(0), \quad P(40)\]
well cuz you base your values off the intervals according to my teacher
what equation would i plug that into?
The original equation.
ok got it
whered you get the P(40) and P(0)
there apart of the domain.. so there possible maxs's mins
oh thats what was meant by end points so if it were aclosed interval i would not take the end points into consideration right?
what are the dimensions of the square based open top box that has a volume of 20 cubic inches and smallest surface area?
can someone help me with this one ^
if you have a new question you should put it in a new thread

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