MATH 200 Study Guide - Lagrange Multiplier, Directional Derivative, Saddle Point

• School: UBC
• Department: Mathematics
• Course: MATH 200
• Professor: All

Document Summary

If two resistors of resistance r1 and r2 are wired in parallel, then the resulting resistance r satis es the equation. Use the linear or di erential approximation to estimate the change in r if r1 decreases from 2 to 1. 9 ohms and. [5%] (b) find the directional derivative of w = f(x, y, z) at p in the direction of the vector. [10: use the second derivative test to nd all values of the constant c for which the function z = x2 + cxy + y2 has a saddle point at (0, 0). Page 6 of 9 pages: let z = f(x, y) where x = 2s + t and y = s t. find the values of the constants a, b. You may assume that z = f(x, y) is a smooth function so that the chain rule and. Clairaut"s theorem on the equality of the mixed partial derivatives apply.