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Q16. Consider the function z = f(x, y) = x² + 16y? + 4. (a) What is the domain and range of f ? Briefly justify your answer. (b) | Draw a contour diagram for f with the level curves k = f(x, y) for k = 4 and k = 20. Show your work and indicate the value of k corresponding to each curve in your diagram. Do not forget the scales on the coordinate axes, and choose the scales so that the curves can be properly drawn and seen. (c) Sketch the trace of f in the xz-plane.

Q16. Consider the function z = f(x, y) = x² + 16y? + 4. (a) What is the domain and range of f ? Briefly justify your answer. (b) | Draw a contour diagram for f with the level curves k = f(x, y) for k = 4 and k = 20. Show your work and indicate the value of k corresponding to each curve in your diagram. Do not forget the scales on the coordinate axes, and choose the scales so that the curves can be properly drawn and seen. (c) Sketch the trace of f in the xz-plane.

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter7: Analytic Trigonometry
Section7.6: The Inverse Trigonometric Functions
Problem 94E
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Q16. Consider the function z = f(x, y) = x² + 16y² + 4. (a) What is the domain and range of f ? Briefly justify your answer. (b) Draw a contour diagram for f with the level curves k = f(x, y) for k 4 and k = 20. Show your work and indicate the value of k corresponding to each curve in your diagram. Do not forget the scales on the coordinate axes, and choose the scales so that the curves can be properly drawn and seen. (c) Sketch the trace of f in the xz-plane. (d) ! . (x, y) = (5, 1). (3, 4) at the point Find the directional derivative of f in the direction of the vector v = Show all your work!
Transcribed Image Text:Q16. Consider the function z = f(x, y) = x² + 16y² + 4. (a) What is the domain and range of f ? Briefly justify your answer. (b) Draw a contour diagram for f with the level curves k = f(x, y) for k 4 and k = 20. Show your work and indicate the value of k corresponding to each curve in your diagram. Do not forget the scales on the coordinate axes, and choose the scales so that the curves can be properly drawn and seen. (c) Sketch the trace of f in the xz-plane. (d) ! . (x, y) = (5, 1). (3, 4) at the point Find the directional derivative of f in the direction of the vector v = Show all your work!
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