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).