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Unformatted text preview: Evan Brown Guido Jo Calculus AP Honors 14 December 2009 Derivative Project 2) The y-values of f(x) are the slope values of f(x), while the x-values remain the same between the two. As f(x) has negative y-values, f(x) has a negative slope. As f(x) has positive y-values, f(x) has a positive slope. Therefore if f(x) goes from negative y- values, crosses the x-axis into positive y-values, f(x)is going from a negative slope to zero, to a positive slope. This change from a negative to zero to positive slope means there will be a minimum. As f(x) goes from positive y-values to negative y-values to negative y-values, f(x) goes from a positive slope, to zero, to a negative slope, creating a maximum. Anytime f(x) crosses the x-axis, which means y-values are zero, there will be extrema. To determine whether the extrema is a maximum or a minimum is based on which direction it crosses the x-axis....
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