Explanation Given: y = 1 1 + | x − 1 | + 1 1 + | x − 4 | f ( x ) = 1 1 + | x − 1 | + 1 1 + | x − 4 | x − 1 = 0 ⇒ x = 1 x − 4 = 0 ⇒ x = 4 t h e l o c a t i o n o f tan g e n t l i n e a t x = 5 2 f ( x ) = 1 1 + | x − 1 | + 1 1 + | x − 4 | f (

3rd Edition

ISBN: 9781464125263

Author: Jon Rogawski, Colin Adams

Publisher: W.H. Freeman & Co

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Rate of Change

The relation between two quantities which displays how much greater one quantity is than another is called ratio.

Slope

The change in the vertical distances is known as the rise and the change in the horizontal distances is known as the run. So, the rise divided by run is nothing but a slope value. It is calculated with simple algebraic equations as:

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Chapter 4.2, Problem 73E

To determine

Find the critical points and extreme values of y=11+|x−1|+11+|x−4|

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Chapter 4.2, Problem 72E

Chapter 4.2, Problem 74E

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1) Give an example of a function whose domain does not include x = -2 or x = 2. 2) Give an example of a function whose domain is [-2, 2]. 3) Give an example of a function whose domain is (-2, 2).

Refer to the graph of the function f in the following figure. = 65 5 -2* (a) Find f(0). f(0) 4 3- 2- 1+ X = (i) f(x) = 3 X = (ii) f(x) = 0 X (b) Find the value of x for which f(x) = 3 and f(x) = 0. X 4 X y = f(x) 5 X

Chapter 4 Solutions

Calculus - Standalone book

Ch. 4.1 - Prob. 1PQ Ch. 4.1 - Prob. 2PQ Ch. 4.1 - Prob. 3PQ Ch. 4.1 - Prob. 4PQ Ch. 4.1 - Prob. 1E Ch. 4.1 - Prob. 2E Ch. 4.1 - Prob. 3E Ch. 4.1 - Prob. 4E Ch. 4.1 - Prob. 5E Ch. 4.1 - Prob. 6E

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Find the critical points and extreme values of y = 1 1 + | x − 1 | + 1 1 + | x − 4 |

Solution Summary: The author explains the solution of f(-5)=1770, the minimum values, and the end-array.

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Find the critical points and extreme values of y=11+|x−1|+11+|x−4|

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