To determine Find the absolute maximum and minimum values of function on the given interval. Graph the function. Show the absolute extreme points and its coordinates on the graph. Explanation Given Information: The given function f ( t ) = | t − 5 | and limit is 4 ≤ t ≤ 7 . Definition: Critical point of function f . An interior point of the domain of a function f where f ′ is zero or undefined is a critical point of f . Calculation: Write the given function. f ( t ) = | t − 5 | = ( t − 5 ) 2 = [ ( t − 5 ) 2 ] 1 2 (1) Find the first derivative [ f ′ ( t ) ] of given function. Differentiate Equation (1) with respect to t . f ′ ( t ) = 1 2 [ ( t − 5 ) 2 ] 1 2 − 1 [ 2 ( t − 5 ) ] = [ ( t − 5 ) 2 ] − 1 2 ( t − 5 ) = t − 5 [ ( t − 5 ) 2 ] 1 2 = t − 5 ( t − 5 ) 2 = t − 5 | t − 5 | (2) Find the value of t ′ ( x ) at t = 5 . Substitute 0 for t in Equation (2). f ′ ( t ) = 5 − 5 | 5 − 5 | = 0 0 = ∞ ( undefined ) The value of t ′ ( x ) is the undefined at t = 5

University Calculus: Early Transcendentals (3rd Edition)

3rd Edition

ISBN: 9780321999580

Author: Joel R. Hass, Maurice D. Weir, George B. Thomas Jr.

Publisher: PEARSON

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Domain

In simple mathematics terms, a domain is defined as the space on which all the possible inputs for the function will lie. It can also be expressed as a set of departures for the required function.

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Chapter 4.1, Problem 36E

To determine

Find the absolute maximum and minimum values of function on the given interval.

Graph the function.

Show the absolute extreme points and its coordinates on the graph.

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Chapter 4.1, Problem 35E

Chapter 4.1, Problem 37E

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Chapter 4 Solutions

University Calculus: Early Transcendentals (3rd Edition)

Ch. 4.1 - In Exercises 16, determine from the graph whether...Ch. 4.1 - In Exercises 1–6, determine from the graph whether...Ch. 4.1 - Prob. 3E Ch. 4.1 - In Exercises 1–6, determine from the graph whether...Ch. 4.1 - Prob. 5E Ch. 4.1 - Prob. 6E Ch. 4.1 - In Exercises 7–10, find the absolute extreme...Ch. 4.1 - In Exercises 7–10, find the absolute extreme...Ch. 4.1 - Prob. 9E Ch. 4.1 - Prob. 10E

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