The table below shows values of differentiable functions, f(x) and g(x), and their derivatives at selected values of x. Use the table of values below to answer each of the questions below. g(x) 2 g'(x) 5 -3 -2 f(x). a. Approximate the value of f'(1.5). Explain why your answer is a good approximation of f'(1.5). f'(x) -1 3 3 3 3 10 4 -1 b. If B(x) = /g(x), what is the equation of the tangent line drawn to B(x) when x = 1? c. If A(x) = x² In(f(x)), what is the value of A'(2)? What does this result say about the behavior of the graph of A(x) when x = 2? Give a reason for your answer.
The table below shows values of differentiable functions, f(x) and g(x), and their derivatives at selected values of x. Use the table of values below to answer each of the questions below. g(x) 2 g'(x) 5 -3 -2 f(x). a. Approximate the value of f'(1.5). Explain why your answer is a good approximation of f'(1.5). f'(x) -1 3 3 3 3 10 4 -1 b. If B(x) = /g(x), what is the equation of the tangent line drawn to B(x) when x = 1? c. If A(x) = x² In(f(x)), what is the value of A'(2)? What does this result say about the behavior of the graph of A(x) when x = 2? Give a reason for your answer.
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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I need help with letter C pleasee
Transcribed Image Text:The table below shows values of differentiable functions, f(x) and g(x), and their derivatives at
selected values of x. Use the table of values below to answer each of the questions below.
f(x)
3
f'(x)
g(x)
g'(x)
a. Approximate the value of f'(1.5). Explain why your
answer is a good approximation of f'(1.5).
-1
3
3
-3
3
1
-2
3
10
4
-1
b. If B(x) = /g(x), what is the equation of the tangent line drawn to B(x) when x = 1?
c. If A(x) = x² In( (x)), what is the value of A'(2)? What does this result say about the behavior of
the graph of A(x) when x = 2? Give a reason for your answer.
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