University:
Seattle Pacific University
Course:
MAT 1236 | Calculus III
Academic year:

2024
Views:

179

Pages:

1
Author:

timddslx2

Workshop #17.5 1. Let f (x, y) = 100 − 2x2 + 2y 2 . (a) Find the critical points of f . (b) Determine whether each critical point is local max, local min, or saddle. Justify your answer without using the second derivative test. (c) Sketch the graph of f and label any extrema. 2. Let f (x, y) = 4x + 2y − 5. Determine whether f has any critical points, then explain your answer geometrically. 3. Let f (x, y) = x2 + 4xy − 8y. Find all critical points, then use the second derivative test to determine whether each is a local max, local min, or saddle. 4. Find the distance from the point (1, 1, −5) to the plane given by 12x + 13y + 5z = −2. Hint: to simplify the computations, minimize the square of the distance to the point. 5. Let f (x, y) = 2y 2 − 4xy + 4x. Let D = {(x, y) | 0 ≤ x ≤ 2, 0 ≤ y ≤ 2}. Sketch D, then find the absolute maximum and minimum values of f on D.