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Math Calculus CALCULUS 4E (LL) W/ ACHIEVE ACCESS

That the function f ( x , y ) = 1 3 x 3 + 2 3 y 3 / 2 − x y satisfies f ( x , y ) ≥ 0 ( x ≥ 0 , y ≥ 0 ) and find the critical points of the function. (a) We need to verify that the set of critical points of f is a parabola y = x 2 and that the second derivative test fails for these points. (b) We need to show that for fixed b , the function g ( x ) = f ( x , b ) is concave up for x > 0 with a critical point at x = b 1 / 2 . (c) We need to conclude that f ( a , b ) ≥ f ( b 1 / 2 , b ) = 0 for all a , b ≥ 0

That the function f ( x , y ) = 1 3 x 3 + 2 3 y 3 / 2 − x y satisfies f ( x , y ) ≥ 0 ( x ≥ 0 , y ≥ 0 ) and find the critical points of the function. (a) We need to verify that the set of critical points of f is a parabola y = x 2 and that the second derivative test fails for these points. (b) We need to show that for fixed b , the function g ( x ) = f ( x , b ) is concave up for x > 0 with a critical point at x = b 1 / 2 . (c) We need to conclude that f ( a , b ) ≥ f ( b 1 / 2 , b ) = 0 for all a , b ≥ 0

Solution Summary: The author determines that the function f (x, y) = 1 3 x 3 + 2 3

CALCULUS 4E (LL) W/ ACHIEVE ACCESS

CALCULUS 4E (LL) W/ ACHIEVE ACCESS

4th Edition

ISBN: 9781319434526

Author: Rogawski

Publisher: MAC HIGHER

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Question

Chapter 15.7, Problem 25E

To determine

That the function $f (x, y) = \frac{1}{3} x^{3} + \frac{2}{3} y^{3 / 2} - x y$ satisfies $f (x, y) \geq 0 (x \geq 0, y \geq 0)$ and find the critical points of the function.

(a) We need to verify that the set of critical points of $f$ is a parabola $y = x^{2}$ and that the second derivative test fails for these points.

(b) We need to show that for fixed $b$ , the function $g (x) = f (x, b)$ is concave up for $x > 0$ with a critical point at $x = b^{1 / 2}$ .

(c) We need to conclude that $f (a, b) \geq f (b^{1 / 2}, b) = 0$ for all $a, b \geq 0$

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Chapter 15.7, Problem 24E

Chapter 15.7, Problem 26E

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Chapter 15 Solutions

CALCULUS 4E (LL) W/ ACHIEVE ACCESS

Ch. 15.1 - Prob. 1PQ Ch. 15.1 - Prob. 2PQ Ch. 15.1 - Prob. 3PQ Ch. 15.1 - Prob. 4PQ Ch. 15.1 - Prob. 5PQ Ch. 15.1 - Prob. 1E Ch. 15.1 - Prob. 2E Ch. 15.1 - Prob. 3E Ch. 15.1 - Prob. 4E Ch. 15.1 - Prob. 5E

Ch. 15.1 - Prob. 6E Ch. 15.1 - Prob. 7E Ch. 15.1 - Prob. 8E Ch. 15.1 - Prob. 9E Ch. 15.1 - Prob. 10E Ch. 15.1 - Prob. 11E Ch. 15.1 - Prob. 12E Ch. 15.1 - Prob. 13E Ch. 15.1 - Prob. 14E Ch. 15.1 - Prob. 15E Ch. 15.1 - Prob. 16E Ch. 15.1 - Prob. 17E Ch. 15.1 - Prob. 18E Ch. 15.1 - Prob. 19E Ch. 15.1 - Prob. 20E Ch. 15.1 - Prob. 21E Ch. 15.1 - Prob. 22E Ch. 15.1 - Prob. 23E Ch. 15.1 - Prob. 24E Ch. 15.1 - Prob. 25E Ch. 15.1 - Prob. 26E Ch. 15.1 - Prob. 27E Ch. 15.1 - Prob. 28E Ch. 15.1 - Prob. 29E Ch. 15.1 - Prob. 30E Ch. 15.1 - Prob. 31E Ch. 15.1 - Prob. 32E Ch. 15.1 - Prob. 33E Ch. 15.1 - Prob. 34E Ch. 15.1 - Prob. 35E Ch. 15.1 - Prob. 36E Ch. 15.1 - Prob. 37E Ch. 15.1 - Prob. 38E Ch. 15.1 - Prob. 39E Ch. 15.1 - Prob. 40E Ch. 15.1 - Prob. 41E Ch. 15.1 - Prob. 42E Ch. 15.1 - Prob. 43E Ch. 15.1 - Prob. 44E Ch. 15.1 - Prob. 45E Ch. 15.1 - Prob. 46E Ch. 15.1 - Prob. 47E Ch. 15.1 - Prob. 48E Ch. 15.1 - Prob. 49E Ch. 15.1 - Prob. 50E Ch. 15.1 - Prob. 51E Ch. 15.1 - Prob. 52E Ch. 15.1 - Prob. 53E Ch. 15.1 - 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Prob. 42E Ch. 15.4 - Prob. 43E Ch. 15.4 - Prob. 44E Ch. 15.4 - Prob. 45E Ch. 15.4 - Prob. 46E Ch. 15.4 - Prob. 47E Ch. 15.5 - Prob. 1PQ Ch. 15.5 - Prob. 2PQ Ch. 15.5 - Prob. 3PQ Ch. 15.5 - Prob. 4PQ Ch. 15.5 - Prob. 5PQ Ch. 15.5 - Prob. 1E Ch. 15.5 - Prob. 2E Ch. 15.5 - Prob. 3E Ch. 15.5 - Prob. 4E Ch. 15.5 - Prob. 5E Ch. 15.5 - Prob. 6E Ch. 15.5 - Prob. 7E Ch. 15.5 - Prob. 8E Ch. 15.5 - Prob. 9E Ch. 15.5 - Prob. 10E Ch. 15.5 - Prob. 11E Ch. 15.5 - Prob. 12E Ch. 15.5 - Prob. 13E Ch. 15.5 - Prob. 14E Ch. 15.5 - Prob. 15E Ch. 15.5 - Prob. 16E Ch. 15.5 - Prob. 17E Ch. 15.5 - Prob. 18E Ch. 15.5 - Prob. 19E Ch. 15.5 - Prob. 20E Ch. 15.5 - Prob. 21E Ch. 15.5 - Prob. 22E Ch. 15.5 - Prob. 23E Ch. 15.5 - Prob. 24E Ch. 15.5 - Prob. 25E Ch. 15.5 - Prob. 26E Ch. 15.5 - Prob. 27E Ch. 15.5 - Prob. 28E Ch. 15.5 - Prob. 29E Ch. 15.5 - Prob. 30E Ch. 15.5 - Prob. 31E Ch. 15.5 - Prob. 32E Ch. 15.5 - Prob. 33E Ch. 15.5 - Prob. 34E Ch. 15.5 - Prob. 35E Ch. 15.5 - Prob. 36E Ch. 15.5 - Prob. 37E Ch. 15.5 - Prob. 38E Ch. 15.5 - 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