18. The graph of the function g on the closed interval [0, 10] consists of four line segments, as shownbelow. Let f be the function defined by f(x)= [ g(t)dt . Find the following values:(8, 5)a. S(3)4.3.(2, 3)(10, 3)(4, 1)b. f'(3)6 7 8 9 103.4Graph of g

Answered: 18. The graph of the function g on the…

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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The function, f(x), in the graph below has f(1) = 1 and f'(1) = = 2. Which of the following are the coordinates of points A and B? A f(x) 1 1.1 Select one: A(1,1) and B(1.1, 1.2) A(1,2) and B(1.1, 1.21) A(1.2,1) and B(1, 2) A(1,1) and B(1.1, 1.21) A(2,1) and B(1.2, 1.1)
5 Suppose this graph represents the function x). At what value(s) of x does f'(x) > 0 and f"(x) = 0? A -1 -2 1 2 0. 6 Suppose this graph represents the function fx). For what value(s) of x does f"(x) = 0 and f"(x) < 0? A -1 -2 1 2
33. (Refer to the graph of f below) Which of the following points can represent a possible point of inflection? yA y= f(x) 2 6 8 x -2 (5, 3) (1, 0) O (4, 2) O (7.-) (7, – 4. 2.
10. Find f and then f: f"(x) = 2-2, f (1) = 0, ƒ(1) = 2
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14. Given the following graph of the function y= f(x), construct the graph of the function y= f"(x). (0,2), (1,3), (2,5), (3,9), (-1,1.5) -8 7- -5 -3 -9 -8 -7 -6 -5 -4 -3 -2 2 6 -2 Solution: https://youtu.be/plmnlQ2nb3g PRESS
3. Suppose that the temperature on a metal plate is given by the function T with T(x, y) = 100 - (x² +4y²) where the temperature is measured in degrees Fahrenheit and a and y are each measured in feet. Now suppose that an ant is walking on the metal plate in such a way that it walks in a straight line from the point (1, 4) to the point (5, 6). (a) Find parametric equations for the ant's a and y coordinates as it walks the line from (1,4) to (5,6) in one minute at a constant speed. (b) What can you say about dr dt and dy dt for every value of t? (c) Determine the instantaneous rate of change in temperature with respect to t that the ant is experi- encing at the moment it is halfway from (1, 4) to (5,6). Include units in your answer.
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18. The graph of the function g on the closed interval [0, 10] consists of four line segments, as shown below. Let f be the function defined by f(x)= [ g(t)dt . Find the following values: (8, 5) a. S(3) 4. 3. (2, 3) (10, 3) (4, 1) b. f'(3) 6 7 8 9 10 3. 4 Graph of g