2. f(x,y) = (x - 1)(x + 2)(x − y) (y + 1)

College Algebra (MindTap Course List)
12th Edition
ISBN:9781305652231
Author:R. David Gustafson, Jeff Hughes
Publisher:R. David Gustafson, Jeff Hughes
Chapter3: Functions
Section3.3: More On Functions; Piecewise-defined Functions
Problem 99E: Determine if the statemment is true or false. If the statement is false, then correct it and make it...
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2 Stationary points
For each of the following functions
. Find the stationary points.
• Using the second derivative test, determine whether the each of these points is a saddle, a minimum
or a maximum.
Note that you must explain every step of your calculations.
1. f(x,y)=³-x+y³-4y
2. f(x,y) = (x - 1)(x+2)(x - y) (y + 1)
3. f(r,0)=sin²0. For this question, you can either use the gradient (and second derivative test)
in polar coordinates, as derived in the videos, OR, convert the function first to Cartesian coordinates,
and then proceed as usual.
Transcribed Image Text:2 Stationary points For each of the following functions . Find the stationary points. • Using the second derivative test, determine whether the each of these points is a saddle, a minimum or a maximum. Note that you must explain every step of your calculations. 1. f(x,y)=³-x+y³-4y 2. f(x,y) = (x - 1)(x+2)(x - y) (y + 1) 3. f(r,0)=sin²0. For this question, you can either use the gradient (and second derivative test) in polar coordinates, as derived in the videos, OR, convert the function first to Cartesian coordinates, and then proceed as usual.
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