Explanation Given: f'' (x) = - f (x) f (x) 2 + f '(x) 2 = f (0) 2 + f '(0) 2 for all g ' (x ) = 2f (x) f ' (x) + 2f '(x) f '' (x) = 2f' (x) (-f(x)) =0 Where we have used the fact that f '' (x) = -f (x) Because g ' (0) = 0 for all x, g (x) = f (x) 2 + f ' (x) 2 must be a constant function in other words f (x) 2 + f '(x) 2 =C for some constant c x = o and find C = f (0) 2 + f '(0) 2 f (x) 2 + f '(x) 2 = f (0) 2 + f '(0) 2 Verify that sin x and cos x sin 2 x + cos 2 x =1 f (x) = sin x

3rd Edition

ISBN: 9781464125263

Author: Jon Rogawski, Colin Adams

Publisher: W.H. Freeman & Co

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Chapter 4.3, Problem 70E

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Show that f (x) satisfies the following equation f '' (x) = - f (x)

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Chapter 4.3, Problem 69E

Chapter 4.3, Problem 71E

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Chapter 4 Solutions

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Show that f (x) satisfies the following equation f '' (x) = - f (x)

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