Explanation Given: f ( x ) = x 2 + r x + s Let, f ( x ) = x 2 + r x + s and assume that the function takes on both positive and negative values so that it will have two roots. From the quadratic equation , the roots of the function is given by x = − r ± r 2 − 4 s 2 It must be noted that the midpoint between the roots is 1 2 ( − r + r 2 − 4 s 2 + −

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ISBN: 9781319055844

Author: FRANZOSA

Publisher: VST

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Chapter 4.2, Problem 87E

To determine

To show that function f(x)=x2+rx+s takes on positive and negative values and its minimum value occurs at the midpoint between the two roots.

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Chapter 4.2, Problem 86E

Chapter 4.2, Problem 88E

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2. Symmetry Evaluate the following integrals using symmetry argu- ments. Let R = {(x, y): -a ≤ x ≤ a, −b ≤ y ≤ b}, where a and b are positive real numbers. a. SS Sf xye xye¯(x² + y²) dA R b. C sin (x − y) - dA x² + y² + 1 R

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Chapter 4 Solutions

EBK CALCULUS

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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To show that function f ( x ) = x 2 + r x + s takes on positive and negative values and its minimum value occurs at the midpoint between the two roots.

Solution Summary: The author explains that the function takes on both positive and negative values and its minimum value occurs at the midpoint between the two roots.

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To show that function f(x)=x2+rx+s takes on positive and negative values and its minimum value occurs at the midpoint between the two roots.

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Chapter 4 Solutions