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College Algebra (MindTap Course List)

College Algebra (MindTap Course List)

12th Edition

ISBN:9781305652231

Author:R. David Gustafson, Jeff Hughes

Publisher:R. David Gustafson, Jeff Hughes

Chapter2: Functions And Graphs

Section2.6: Proportion And Variation

Problem 17E: Find the constant of proportionality. y is directly proportional to x. If x=30, then y=15.

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Question

Given f(x, y) = (3x – x²)(2y – y²).
-
-
(a) Find all the critical points of the function.
(b) Classify each critical point as a local maximum, a local minimum or a saddle point
using the Second Derivatives Test.

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2. Given f(x, y) = 2x – 3y? + 6xy – 12x. (i) Find critical points of f. (ii) Use the second derivative test to determine whether cach critical point is a local maximum, a local minimum or a saddle point.
For a function f (x, y), (0, 0) and (1, 1) are two critical points. Also, fxx = 2x², fyy = y² and fxy = -1. Apply the Second Derivative Test to determine the extremum nature of these two critical points.
Let g(x, y) = In x + 2 In y - x-8y . Find the critical points. use the second Derivative Test to determine if the critical points are relative minima, maxima or saddle points. Show all of the steps
Identify any critical points, and use the second derivative test to determine whether each critical point is a maximum, minimum, saddle point, or none of these. (Order your answers from smallest to largest x, then from smallest to largest y.) f(x, y) = x3 + y³ - 300x - 108y - 5 (х, у, 2) %3D -10, – 6,2160 maximum (х, у, 2) %3D -10,6,2160 saddle point v (х, у, 2) %3 10, – 6, – 2160 saddle point v (x, y, z) = 10,6, – 2160 minimum
2. Given f(x, y) = 2.x³ – 3y² – 6xy – 12x. - (i) Find critical points of f. (ii) Use the second derivative test to determine whether the critical point is a local maximum, a local minimum or a saddle point.

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