Can anybody help me with this maths problem? It's about applications of differentiation by using de dy/dx notation.
2006-12-03 08:24:28 · 5 answers · asked by Anonymous in Science & Mathematics ➔ Mathematics
We know x + y = 12, or y = 12-x.
Substitute that into the product: P = xy = x(12-x) = 12x - x^2.
Now differentiate: dP/dx = 12 - 2x.
Make equal to 0: x = 6.
So x = 6, y = 6, xy = 36.
2006-12-03 08:26:13 · answer #1 · answered by stephen m 4 · 2⤊ 0⤋
Product, P = xy
and x+y = 12
so y=12-x
so P = x(12-x) = 12x-x^2
By calculus, max P occurs when dP/dx = 0
dP/dx = 12 - 2x
hence dP/dx = 0 when x = 6
therefore y = 6 and P = 36
NB this is proof that for two variables max value occurs when x is as close to y as possible. ie to have a maximum area from the same perimeter a square is the answer.
2006-12-03 08:27:56 · answer #2 · answered by ? 7 · 0⤊ 0⤋
The real numbers are 6 and 6 and their product is 36.
2006-12-03 08:57:39 · answer #3 · answered by fadiga 2 · 0⤊ 0⤋
is it 6 + 6??
2006-12-03 08:26:01 · answer #4 · answered by Bridget J. ♥ 4 · 0⤊ 0⤋
theory is a theory interior the style of electro-chemical reactions which offer the philosopher the sensation of existence and reality. HAHAHAHAHAHAHA!!! only a theory............ :)
2016-11-23 14:50:46 · answer #5 · answered by nations 4 · 0⤊ 0⤋