Chapter 7: Problem 30
Find the limit. $$ \lim _{x \rightarrow 4} \sqrt[3]{x+4} $$
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The ordering and transportation cost \(C\) per unit for the components used in manufacturing a product is \(C=\left(375,000+6 x^{2}\right) / x, \quad x \geq 1\) where \(C\) is measured in dollars and \(x\) is the order size. Find the rate of change of \(C\) with respect to \(x\) when (a) \(x=200\), (b) \(x=250\), and (c) \(x=300\). Interpret the meaning of these values.
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) \(p=-f(x)+5\)
Find the derivative of the function. State which differentiation rule(s) you used to find the derivative. $$ f(x)=x\left(1-\frac{2}{x+1}\right) $$
Identify the inside function, \(u=g(x)\), and the outside function, \(y=f(u)\). $$ y=f(g(x)) \quad u=g(x) \quad y=f(u) $$ $$ y=(3 x+1)^{-1} $$
Find the derivative of the function. State which differentiation rule(s) you used to find the derivative. $$ y=t \sqrt{t+1} $$
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