ОP 7 1. Consider the functions f(x) = x2 and g(x) = Vx. 1. Use linear approximation to approximate the value of f(3.01). 2. Use a calculator to find the actual value of f(3.01). Is this value larger or smaller than your approximated value? 3. Use linear approximation to approximate the value of g(4.01)? 4. Use a calculator to find the actual value of g(4.01). Is this value larger or smaller than your approximated value? 5. Now, we'll try to explain what's happening here. Compute the functions f"(x) and g"(x). What do you notice about these functions? Are they positive or negative? 6. Using the fact that the second derivative is the rate of change of the first derivative, explain why your approximated answers were larger or smaller than the actual functions values for the functions f and g above. 2. A circular oil spill on the ocean surface has radius r = 10 Km. Make sure to

Functions and Change: A Modeling Approach to College Algebra (MindTap Course List)
6th Edition
ISBN:9781337111348
Author:Bruce Crauder, Benny Evans, Alan Noell
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Chapter1: Functions
Section1.2: Functions Given By Tables
Problem 32SBE: Does a Limiting Value Occur? A rocket ship is flying away from Earth at a constant velocity, and it...
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Problem 1 Parts 1, 2, and 3

ОP 7
1. Consider the functions f(x) = x2 and g(x) = Vx.
1. Use linear approximation to approximate the value of f(3.01).
2. Use a calculator to find the actual value of f(3.01). Is this value larger or
smaller than your approximated value?
3. Use linear approximation to approximate the value of g(4.01)?
4. Use a calculator to find the actual value of g(4.01). Is this value larger or
smaller than your approximated value?
5. Now, we'll try to explain what's happening here. Compute the functions
f"(x) and g"(x). What do you notice about these functions? Are they
positive or negative?
6. Using the fact that the second derivative is the rate of change of the first
derivative, explain why your approximated answers were larger or smaller
than the actual functions values for the functions f and g above.
2. A circular oil spill on the ocean surface has radius r = 10 Km. Make sure to
Transcribed Image Text:ОP 7 1. Consider the functions f(x) = x2 and g(x) = Vx. 1. Use linear approximation to approximate the value of f(3.01). 2. Use a calculator to find the actual value of f(3.01). Is this value larger or smaller than your approximated value? 3. Use linear approximation to approximate the value of g(4.01)? 4. Use a calculator to find the actual value of g(4.01). Is this value larger or smaller than your approximated value? 5. Now, we'll try to explain what's happening here. Compute the functions f"(x) and g"(x). What do you notice about these functions? Are they positive or negative? 6. Using the fact that the second derivative is the rate of change of the first derivative, explain why your approximated answers were larger or smaller than the actual functions values for the functions f and g above. 2. A circular oil spill on the ocean surface has radius r = 10 Km. Make sure to
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