Suppose f 1x, y2 5 4x2 1 3y2

.

a. Calculate the partial derivatives of f.

b. Suppose f 1x, y2 5 16. Use the implicit function theorem to calculate dy/dx.

c. What is the value of dy/dx if x 5 1, y 5 2?

d. Graph your results and use it to interpret the results in parts

(b) and

(c) of this problem.