The first quadrant of the x y coordinate plane is given. There is one curve on the graph. The curve starts at the point (0, 600), goes down and right becoming less steep, passes through the approximate points (10, 400), (20, 300) and (30, 250), and reaches a minimum at the point (40, 200). The curve then goes up and right becoming more steep, passes through the approximate points (50, 400) and (60, 700), becoming less steep, reaches a maximum at the approximate point (70, 900) where it changes direction and goes down and right. The curve exits the window at the XX point (80, 800).20" 40 60 The graph of a function f is shown. y 800 400 x 0 20 40 60 (a) Find the average rate of change of f on the interval [50, 60]. (b) Identify an interval on which the average rate of change of f is 0. ○ [10, 50] [10, 40] ○ [20, 40] ○ [0, 80] ○ [0, 60] (c) Compute the following. f(40) - f(0) 40 0 What does this value represent geometrically? the slope of the tangent line at (20, f(20)) ◇ the slope of the line segment from (0, f(0)) to (40, f(40)) O the slope of the tangent line at (40, f(40)) the slope of the tangent line at (0, f(0)) (d) Estimate the value of f' (50). (e) Is f'(10) > f'(30)? Yes No f(80) - f(40), (f) Is f'(60) > 80-40 Yes No Explain. The slope of the tangent line at x = 60, f'(60), is less than the slope of the line passing through (40, f(40)) and (80, f(80)). The slope of the tangent line at x = 40, f'(40), is less than the slope of the line passing through (60, f(60)) and (80, f(80)). The slope of the tangent line at x = 60, f'(60), is greater than the slope of the line passing through (40, f(40)) and (80, f(80)). The slope of the tangent line at x = 80, f'(80), is greater than the slope of the line passing through (40, f(40)) and (60, f(60)). The slope of the tangent line at x = 80, f'(80), is less than the slope of the line passing through (40, f(40)) and (60, f(60)).
The first quadrant of the x y coordinate plane is given. There is one curve on the graph. The curve starts at the point (0, 600), goes down and right becoming less steep, passes through the approximate points (10, 400), (20, 300) and (30, 250), and reaches a minimum at the point (40, 200). The curve then goes up and right becoming more steep, passes through the approximate points (50, 400) and (60, 700), becoming less steep, reaches a maximum at the approximate point (70, 900) where it changes direction and goes down and right. The curve exits the window at the XX point (80, 800).20" 40 60 The graph of a function f is shown. y 800 400 x 0 20 40 60 (a) Find the average rate of change of f on the interval [50, 60]. (b) Identify an interval on which the average rate of change of f is 0. ○ [10, 50] [10, 40] ○ [20, 40] ○ [0, 80] ○ [0, 60] (c) Compute the following. f(40) - f(0) 40 0 What does this value represent geometrically? the slope of the tangent line at (20, f(20)) ◇ the slope of the line segment from (0, f(0)) to (40, f(40)) O the slope of the tangent line at (40, f(40)) the slope of the tangent line at (0, f(0)) (d) Estimate the value of f' (50). (e) Is f'(10) > f'(30)? Yes No f(80) - f(40), (f) Is f'(60) > 80-40 Yes No Explain. The slope of the tangent line at x = 60, f'(60), is less than the slope of the line passing through (40, f(40)) and (80, f(80)). The slope of the tangent line at x = 40, f'(40), is less than the slope of the line passing through (60, f(60)) and (80, f(80)). The slope of the tangent line at x = 60, f'(60), is greater than the slope of the line passing through (40, f(40)) and (80, f(80)). The slope of the tangent line at x = 80, f'(80), is greater than the slope of the line passing through (40, f(40)) and (60, f(60)). The slope of the tangent line at x = 80, f'(80), is less than the slope of the line passing through (40, f(40)) and (60, f(60)).
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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Transcribed Image Text:The first quadrant of the x y coordinate plane is given.
There is one curve on the graph. The curve starts at
the point (0, 600), goes down and right becoming less
steep, passes through the approximate points
(10, 400), (20, 300) and (30, 250), and reaches a
minimum at the point (40, 200). The curve then goes
up and right becoming more steep, passes through the
approximate points (50, 400) and (60, 700), becoming
less steep, reaches a maximum at the approximate
point (70, 900) where it changes direction and goes
down and right. The curve exits the window at the XX
point (80, 800).20"
40
60
![The graph of a function f is shown.
y
800
400
x
0
20
40
60
(a) Find the average rate of change of f on the interval [50, 60].
(b) Identify an interval on which the average rate of change of f is 0.
○ [10, 50]
[10, 40]
○ [20, 40]
○ [0, 80]
○ [0, 60]
(c) Compute the following.
f(40) - f(0)
40 0
What does this value represent geometrically?
the slope of the tangent line at (20, f(20))
◇ the slope of the line segment from (0, f(0)) to (40, f(40))
O the slope of the tangent line at (40, f(40))
the slope of the tangent line at (0, f(0))
(d) Estimate the value of f' (50).
(e) Is f'(10) > f'(30)?
Yes
No
f(80) - f(40),
(f) Is f'(60) >
80-40
Yes
No
Explain.
The slope of the tangent line at x = 60, f'(60), is less than the slope of the line passing through (40, f(40)) and (80, f(80)).
The slope of the tangent line at x = 40, f'(40), is less than the slope of the line passing through (60, f(60)) and (80, f(80)).
The slope of the tangent line at x = 60, f'(60), is greater than the slope of the line passing through (40, f(40)) and (80, f(80)).
The slope of the tangent line at x = 80, f'(80), is greater than the slope of the line passing through (40, f(40)) and (60, f(60)).
The slope of the tangent line at x = 80, f'(80), is less than the slope of the line passing through (40, f(40)) and (60, f(60)).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Faf796a3f-89a1-43bc-8a62-1872a1a105f0%2F9ddb88d7-7b9a-4e79-b6f3-4466d07176c8%2Fi4fhqk_processed.jpeg&w=3840&q=75)
Transcribed Image Text:The graph of a function f is shown.
y
800
400
x
0
20
40
60
(a) Find the average rate of change of f on the interval [50, 60].
(b) Identify an interval on which the average rate of change of f is 0.
○ [10, 50]
[10, 40]
○ [20, 40]
○ [0, 80]
○ [0, 60]
(c) Compute the following.
f(40) - f(0)
40 0
What does this value represent geometrically?
the slope of the tangent line at (20, f(20))
◇ the slope of the line segment from (0, f(0)) to (40, f(40))
O the slope of the tangent line at (40, f(40))
the slope of the tangent line at (0, f(0))
(d) Estimate the value of f' (50).
(e) Is f'(10) > f'(30)?
Yes
No
f(80) - f(40),
(f) Is f'(60) >
80-40
Yes
No
Explain.
The slope of the tangent line at x = 60, f'(60), is less than the slope of the line passing through (40, f(40)) and (80, f(80)).
The slope of the tangent line at x = 40, f'(40), is less than the slope of the line passing through (60, f(60)) and (80, f(80)).
The slope of the tangent line at x = 60, f'(60), is greater than the slope of the line passing through (40, f(40)) and (80, f(80)).
The slope of the tangent line at x = 80, f'(80), is greater than the slope of the line passing through (40, f(40)) and (60, f(60)).
The slope of the tangent line at x = 80, f'(80), is less than the slope of the line passing through (40, f(40)) and (60, f(60)).
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