Consider the function f : R 2 → R: f(x, y) = ax^2 + by^2 , where a and b are real constants. (a) Assume a, b > 0. Sketch a contour plot for the function f, including the level set at 1. (b) Assume a > 0 and b < 0. Sketch a contour plot, including the level set at 1. (c) Describe the level set at 1 when a = 0, b ̸= 0 and when a ̸= 0, b = 0.
Consider the function f : R 2 → R: f(x, y) = ax^2 + by^2 , where a and b are real constants. (a) Assume a, b > 0. Sketch a contour plot for the function f, including the level set at 1. (b) Assume a > 0 and b < 0. Sketch a contour plot, including the level set at 1. (c) Describe the level set at 1 when a = 0, b ̸= 0 and when a ̸= 0, b = 0.
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter9: Multivariable Calculus
Section9.3: Maxima And Minima
Problem 19E
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Consider the function f : R 2 → R: f(x, y) = ax^2 + by^2 , where a and b are real constants. (a) Assume a, b > 0. Sketch a contour plot for the function f, including the level set at 1. (b) Assume a > 0 and b < 0. Sketch a contour plot, including the level set at 1. (c) Describe the level set at 1 when a = 0, b ̸= 0 and when a ̸= 0, b = 0.
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