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Chapter 7: Problem 6
Find the derivative of the function. $$ f(x)=-2 $$
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The ordering and transportation cost \(C\) per unit (in thousands of dollars) of the components used in manufacturing a product is given by $$ C=100\left(\frac{200}{x^{2}}+\frac{x}{x+30}\right), \quad 1 \leq x $$ where \(x\) is the order size (in hundreds). Find the rate of change of \(C\) with respect to \(x\) for each order size. What do these rates of change imply about increasing the size of an order? Of the given order sizes, which would you choose? Explain. (a) \(x=10\) (b) \(x=15\) (c) \(x=20\)
Consumer Awareness The prices per pound of lean and extra lean ground beef in the United States from 1998 to 2005 can be modeled by \(P=\frac{1.755-0.2079 t+0.00673 t^{2}}{1-0.1282 t+0.00434 t^{2}}, \quad 8 \leq t \leq 15\) where \(t\) is the year, with \(t=8\) corresponding to 1998 . Find \(d P / d t\) and evaluate it for \(t=8,10,12\), and 14 . Interpret the meaning of these values.
Find the derivative of the function. State which differentiation rule(s) you used to find the derivative. $$ f(x)=x^{3}(x-4)^{2} $$
Find the derivative of the function. State which differentiation rule(s) you used to find the derivative. $$ y=-\frac{4}{(t+2)^{2}} $$
Use the given information to find \(f^{\prime}(2)\) \(g(2)=3\) and \(g^{\prime}(2)=-2\) \(h(2)=-1 \quad\) and \(\quad h^{\prime}(2)=4\) $$ f(x)=2 g(x)+h(x) $$
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