Exam 3 solution

# We need to determine if method 1 study the sign of x

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Unformatted text preview: if Method #1: Study the sign of x-values sample number . and qualify is the location of a max or a min or neither. There are two ways to do that: on the interval . sign of conclusion about is decreasing has horizontal tangent line is increasing We see that on the interval the graph of is decreasing until , then increasing after . So the critical value is the location of the absolute min for the interval . But remember the absolute min is the y-value, not the x-value. We substitute into to get a y-value. The result: . Conclude that the absolute min is . (It occurs at .) Method #2: Study the sign of the interval . So far, we have found that . Therefore, . We see that for all , the value of will be positive. So the graph of must be concave up for all . So the critical value is the location of the absolute min for the interval . As we did in the previous method, we find the value of the absolute min to be . [5] (suggested exercise 5-6#11) A company manufactures and sells hats. The demand is the number of hats made each day. The price is the selling price for each hat (in dollars). The daily price-demand equation is . Remember that . The Cost function is (in dollars). Remember that . (A) Graph the price-demand equation and find its domain. Explain how you know the domain. Solution: The graph of the equation will be a line with slope . The vertical axis intercept will be at the point ; the horizontal axis intercept will be at the point . If we considered the equation as an abstract mathematical equation, its domain would be the set of all real numbers . But the equation is not just an abstract mathematical equation: it is modeling the making and selling of hats. Because one cannot make a negative number of hats, we know that is restricted to . And because price cannot be negative...
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## This document was uploaded on 02/17/2014 for the course MATH 1350 at Ohio University- Athens.

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