## Tutoring on Relative Extrema and Applications to Functions of Two Variables

Learning Objectives:

#### Understand and Apply Relative Extrema and Applications to Functions of Two variables.

Math Tutoring on Relative Extrema and Applications to Functions of Two Variables

Informally, we can think of a Relative Extrema as a high point or low point on the surface defined by .

A function has a Relative Minimum at the point  if  in some region containing .

A function has a Relative Maximum at the point  if  in some region containing .

Steps to Determine Relative Extrema in Math Tutoring:

1.     Locate the Critical Numbers.

2.     Perform a second partials test.

·        If , then ‘f’ has a Relative Minimum at    (a, b).

·        If , then f has a Relative Maximum at   (a, b).

·        If  is a Saddle Point.

·        The test is inconclusive if d = 0.

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Hook Questions:

1.     Define Relative Extrema.

2.     What are the steps to determine Relative Extrema?

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