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How can you maximize your happiness under a budget? When does a function reach its minimum value? When does a curve change direction? The calculus of extrema explains these "extreme" situations.

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The above diagram shows the curve \(y=f(x).\) Let \(a\) be the \(x\)-coordinate of the intersection point between the curve and negative part of the \(x\)-axis, and let \(b\) and \(c\) be the \(x\)-coordinates of the local maximum and minimum of the curve, respectively, as shown in the diagram. If \[a = -3, b = 4, c = 7, \] and \(f'(x)>0\) for the portions of the curve that are not displayed in the diagram, what is the range of \(x\) that satisfies \(f(x)f'(x) > 0?\)

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