
Critical Points and Extrema in Multivariable Functions

Interactive Video
•
Mathematics
•
10th - 12th Grade
•
Hard
Standards-aligned

Amelia Wright
FREE Resource
Standards-aligned
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10 questions
Show all answers
1.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the significance of critical points in functions of two variables?
They are points where the function is undefined.
They always indicate a maximum value.
They are points where the function is continuous.
They are potential locations for relative extrema.
2.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the partial derivative of the function f(x, y) = 4x^2 - 6x - 6y + 3y^2 with respect to x?
8x - 6
4x - 6
6x - 4
8x + 6
3.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
When finding the partial derivative with respect to y, what is treated as a constant?
x
y
Neither x nor y
Both x and y
Tags
CCSS.7.EE.B.4A
4.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
How do you solve the equation 8x - 6 = 0 for x?
x = 2/3
x = 1/2
x = 3/4
x = 6/8
5.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the y-coordinate of the critical point found in the function?
3
2
1
0
6.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the next step after finding the critical point (3/4, 1) in the function?
Check for continuity.
Perform the second partials test.
Find the z-coordinate by substituting into the function.
Graph the function.
7.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the z-coordinate of the critical point (3/4, 1) on the surface?
-21/4
-3/4
0
1/4
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