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**NandP** The derivative of a function f is given by f'(x) = (x^3-2x)(cos x) for 0 ≤ x ≤ 2.

a. Find the x-coordinate of the relative minimum of f(x). You may use your calculator, but show the analysis that leads to your conclusion.

**a relative max occurs where f'(x) changes sign from positive to negative**

b. Find the x-coordinate of each point of inflection on the graph f(x). Justify your answer.

**an inflection point occurs on the graph of f(x) wherever f'(x) changes the sign of its slope**

c. Find the x-coordinate of the point at which f(x) attains an absolute maximum. Justify your answer.

**absolute extrema may occur at relative extrema, **__or at an endpoint__.

**note that the graph of f'(x) is mostly negative**