Explanation Given : The function is f ( x ) = x x 2 + 4 . Calculation: Derivate the function with respect to x as follows: d d x f ( x ) = d d x ( x x 2 + 4 ) f ′ ( x ) = ( x 2 + 4 ) − x ( 2 x ) ( x 2 + 4 ) 2 = − x 2 + 4 ( x 2 + 4 ) 2 For increasing interval of the function, f ′ ( x ) > 0 − x 2 + 4 ( x 2

14th Edition

ISBN: 9781464151088

Author: Associate Professor Laura Taalman, Peter Kohn

Publisher: W.H. Freeman & Company

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Chapter 3.2, Problem 29S

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To find: The interval in which function is increasing or decreasing and verification from its graph.

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Chapter 3.2, Problem 28S

Chapter 3.2, Problem 30S

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4 Consider f(x) periodic function with period 2, coinciding with (x) = -x on the interval [,0) and being the null function on the interval [0,7). The Fourier series of f: (A) does not converge in quadratic norm to f(x) on [−π,π] (B) is pointwise convergent to f(x) for every x = R П (C) is in the form - 4 ∞ +Σ ak cos(kx) + bk sin(kx), ak ‡0, bk ‡0 k=1 (D) is in the form ak cos(kx) + bk sin(kx), ak 0, bk 0 k=1

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The interval in which function is increasing or decreasing and verification from its graph.

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