In this problem, you will investigate the family of functions h(x) = x + cos(ax) , where a is a positive constant such that 0 < a < 4.

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A. Graph the curves y(x) = x + cos(¼x) and y(x) = x + cos(4x)

B. For what values of a will h(x) have a relative maximum at x = 1?

C. Which values of a make h(x) strictly decreasing? Justify your answer.

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