Calculus 3: Exhaustive Final Review (Ch 14 & 16)
Section 14.7: Max/Min & Saddle Points
1. f(x, y) = x^2 + xy + y^2 + y
2. f(x, y) = xy 2x 2y x^2 y^2
3. f(x, y) = (x y)(1 xy)
4. f(x, y) = x^4 + y^4 4xy + 1
5. f(x, y) = e^x cos(y)
6. f(x, y) = y cos(x), on [0, 2] × [0, 2]
7. Find absolute max/min of f(x, y) = x^2 + y^2 2x on triangle with vertices (2,0), (0,2), (0,2).
8. Find absolute max/min of f(x, y) = 3 + xy x 2y on region bounded by y = x^2 and y = 4.
9. Find three positive numbers whose sum is 100 and maximize the product.
10. Find the volume of the largest rectangular box in the first octant with one vertex on x + 2y + 3z
= 6.
