Q1 Fall 2004

Q1:  Use partial derivatives to determine the slope of the the equation 2x³y⁴ = 5.

A1:  The slope is dy/dx=- df/dx / df/dy = -(3*2x²y⁴) / (4*2x³y³) = -3y/4x

Q2:  Find where y=2x and 2y=30-2x.  

A2:  Using the fact that y=2x we can rewrite the second equation as 2(2x)=30-2x or 4x=30-2x or 6x=30 or x=5.  Plugging this into either equation gives y=10.  The solution is (5,10).