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Finding Absolute Extrema and Critical Points

Finding Absolute Extrema and Critical Points

Assessment

Interactive Video

Mathematics

11th Grade - University

Practice Problem

Hard

CCSS
HSF.IF.A.2

Standards-aligned

Created by

Aiden Montgomery

FREE Resource

Standards-aligned

CCSS.HSF.IF.A.2
This video tutorial explains how to find the absolute maximum and minimum values of a multivariable function defined on a rectangle. It covers calculating partial derivatives, solving for critical points, and evaluating function values along line segments. The tutorial concludes by identifying the absolute extrema using a table of values.

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10 questions

Show all answers

1.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the first step in finding the absolute extrema of a multivariable function?

Find the partial derivatives

Evaluate the function at endpoints

Determine the critical points

Draw the function graph

2.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

How do you find the critical points of a multivariable function?

By drawing a graph of the function

By evaluating the function at the endpoints

By setting each partial derivative equal to zero

By setting the function equal to zero

Tags

CCSS.HSF.IF.A.2

3.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

In the first line segment analysis, what is the function value at x=4?

12

0

16

4

4.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

For the second line segment, what is the function value when y=3?

4

12

16

0

5.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What type of function is analyzed in the third line segment?

Logarithmic

Exponential

Quadratic

Linear

6.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the function value at the critical point (2, 2)?

8

4

16

0

7.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the absolute maximum value of the function?

0

16

4

12

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