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In this lesson, we will learn how to find local maxima and minima of functions with more than one variable, using tests with first and second derivatives.

Q1:

Find all stationary points of the function π ( π₯ , π¦ ) = π₯ + 2 π¦ , stating whether they are minima, maxima, or saddle points.

Q2:

Find all stationary points of the function π ( π₯ , π¦ ) = π₯ β 3 π₯ + π¦ β 3 π¦ 3 3 .

Q3:

Find all local maxima and minima of the function π ( π₯ , π¦ ) = π₯ β 3 π₯ + π¦ 3 2 .

Q4:

Find all stationary points of the function π ( π₯ , π¦ ) = 4 π₯ β 4 π₯ π¦ + 2 π¦ + 1 0 π₯ β 6 π¦ 2 2 , stating whether they are minima, maxima, or saddle points.

Q5:

Find all stationary points of the function π ( π₯ , π¦ ) = 2 π₯ β 6 π₯ π¦ + π¦ 3 2 , stating whether they are minima, maxima, or saddle points.

Q6:

Find all stationary points of the function π ( π₯ , π¦ ) = 2 π₯ + 6 π₯ π¦ + 3 π¦ 3 2 , stating whether they are minima, maxima, or saddle points.

Q7:

Find all stationary points of the function π ( π₯ , π¦ ) = π₯ β 1 2 π₯ + π¦ + 8 π¦ 3 2 , stating whether they are minima, maxima, or saddle points.

Q8:

Find all stationary points of the function π ( π₯ , π¦ ) = π₯ + 3 π₯ + π¦ β 3 π¦ 3 2 3 2 , stating whether they are minima, maxima, or saddle points.

Q9:

Find all stationary points of the function π ( π₯ , π¦ ) = β 4 π₯ + 4 π₯ π¦ β 2 π¦ + 1 6 π₯ β 1 2 π¦ 2 2 , stating whether they are minima, maxima, or saddle points.

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