Chapter 7: Problem 6
Find the derivative of the function. $$ f(x)=-2 $$
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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. $$ g(x)=\left(\frac{x-3}{x+4}\right)\left(x^{2}+2 x+1\right) $$
Given \(f(x)=x+1\), which function would most likely represent a demand function? Explain your reasoning. Use a graphing utility to graph each function, and use each graph as part of your explanation. (a) \(p=f(x)\) (b) \(p=x f(x)\) (c) \(p=-f(x)+5\)
Identify the inside function, \(u=g(x)\), and the outside function, \(y=f(u)\). $$ y=f(g(x)) \quad u=g(x) \quad y=f(u) $$ $$ y=\left(4-x^{2}\right)^{-1} $$
Use the General Power Rule to find the derivative of the function. $$ f(t)=\sqrt{t+1} $$
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