Explanation Given: The given function is y = 2 x 2 + 4 x + 5 . Calculation: Given:the given interval is [ 0 , 2 ] . Use sum rule . ( f + g ) ' = f ' + g ' y = 2 x 2 + 4 x + 5 y ' = d d x ( 2 x 2 ) + d d x ( 4 x ) + d d x ( 5 ) = 4 x + 4 For critical point y ' = 0 . 4 x + 4 = 0 ⇒ 4 x + 4 − 4 = 0 − 4 ⇒ 4 x = − 4 ⇒ 4 4 x = −

4th Edition

ISBN: 9781319050740

Author: Jon Rogawski, Colin Adams, Robert Franzosa

Publisher: W. H. Freeman

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Question

Chapter 4.2, Problem 28E

To determine

Find theminimum and maximum values of the given functionin the given interval by comparing with critical and end points.

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Chapter 4.2, Problem 27E

Chapter 4.2, Problem 29E

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A factorization A = PDP 1 is not unique. For A= 7 2 -4 1 1 1 5 0 2 1 one factorization is P = D= and P-1 30 = Use this information with D₁ = to find a matrix P₁ such that - -1 -2 0 3 1 - - 1 05 A-P,D,P P1 (Type an integer or simplified fraction for each matrix element.)

Matrix A is factored in the form PDP 1. Use the Diagonalization Theorem to find the eigenvalues of A and a basis for each eigenspace. 30 -1 - 1 0 -1 400 0 0 1 A= 3 4 3 0 1 3 040 3 1 3 0 0 4 1 0 0 003 -1 0 -1 Select the correct choice below and fill in the answer boxes to complete your choice. (Use a comma to separate vectors as needed.) A basis for the corresponding eigenspace is { A. There is one distinct eigenvalue, λ = B. In ascending order, the two distinct eigenvalues are λ₁ ... = and 2 = Bases for the corresponding eigenspaces are { and ( ), respectively. C. In ascending order, the three distinct eigenvalues are λ₁ = = 12/2 = and 3 = Bases for the corresponding eigenspaces are {}, }, and { respectively.

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Chapter 4 Solutions

Calculus: Early Transcendentals

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 theminimum and maximum values of the given functionin the given interval by comparing with critical and end points.

Solution Summary: The author calculates the minimum and maximum values of the given function by comparing with critical and end points.

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Find theminimum and maximum values of the given functionin the given interval by comparing with critical and end points.

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Chapter 4 Solutions