

Local Linearization and Derivatives
Interactive Video
•
Mathematics
•
11th - 12th Grade
•
Practice Problem
•
Hard
Liam Anderson
FREE Resource
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10 questions
Show all answers
1.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the function F(x) defined as in the video?
The square of the natural log of x
The natural log of x squared
The exponential of x
The natural log of x
2.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the point of linearization for the function F(x)?
x = e
x = 0
x = 1
x = 2
3.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What does the local linearization L(x) represent?
A quadratic approximation of F(x)
The derivative of F(x)
The original function F(x)
A linear approximation of F(x) around a point
4.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
How is the slope of the tangent line at a point used in local linearization?
It is added to the function value
It is multiplied by the difference between x and the point of linearization
It is used to find the y-intercept
It is ignored
5.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the derivative of the natural log of x squared?
1/x
2/x
1/x^2
2x
6.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the value of F(e) for the function F(x) = ln(x^2)?
0
e
1
2
7.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the formula for L(x) in terms of F(a) and the derivative?
L(x) = F(a) - F'(a) * (x - a)
L(x) = F(a) * F'(a) * (x - a)
L(x) = F(a) + F'(a) * (x - a)
L(x) = F(a) / F'(a) * (x - a)
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