Posted by julie on .
given y = 4x3
find the minimum value of xy.
find the rate of change of xy with respect to x.
find the rate of change of xy with respect to y.

calculus 
Damon,
f(x,y) = xy = x (4x3)
f = 4 x^2  3x
df/dx = 8 x  3
that is 0 when x = 3/8 and the second derivative is positive so it is a minumum
then x y = (3/8)(3/2 3)
= (3/8) (3/2) = 9/16
we found df/dx
now df/dy
4x = y+3
x = (y+3)/4
g(y) = xy = y(y+3)/4
= (1/4)(y^2+3y)
dg/dy = (1/4)(2 y+3)
= y/2 + 3/4