Show is a contour plot for a function z = 3 В A (a) Is fy positive, negative, or zero at A? (b) Is fæx positive, negative, or zero at B? Copy the contour plot onto your own paper. (c) The function f has exactly two critical points in the region pictured. Mark these in the contour plot, label them P and Q, and identify whether each is a local minimum, local maximum, or saddle point. (d) Sketch the gradient of f at A in the contour plot.
Show is a contour plot for a function z = 3 В A (a) Is fy positive, negative, or zero at A? (b) Is fæx positive, negative, or zero at B? Copy the contour plot onto your own paper. (c) The function f has exactly two critical points in the region pictured. Mark these in the contour plot, label them P and Q, and identify whether each is a local minimum, local maximum, or saddle point. (d) Sketch the gradient of f at A in the contour plot.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:Show is a contour plot for a function z = f(x,y).
3
3
1
A
2
(a) Is fy positive, negative, or zero at A?
(b) Is fæx positive, negative, or zero at B?
Copy the contour plot onto your own paper.
(c) The function f has exactly two critical points in the region pictured. Mark these in the contour
plot, label them P and Q, and identify whether each is a local minimum, local maximum, or saddle
point.
(d) Sketch the gradient of f at A in the contour plot.
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