calculus
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.

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