Q1 Fall 2004

Q1: Use partial derivatives to determine the slope of the the equation
2x^{3}y^{4} = 5.

A1: The slope is dy/dx=- *df/dx* / *df/dy *= -(3*2x^{2}y^{4})
/ (4*2x^{3}y^{3}) = -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).