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Chapter 7: Problem 22
Find the derivative of the function. $$ s(t)=4 t^{-1}+1 $$
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Find an equation of the tangent line to the graph of the function at the given point. Then use a graphing utility to graph the function and the tangent line in the same viewing window. $$ f(t)=\left(t^{2}-9\right) \sqrt{t+2} \quad(-1,-8) $$
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) \(x=20\)
Find the derivative of the function. State which differentiation rule(s) you used to find the derivative. $$ y=\frac{1}{\sqrt{x+2}} $$
Use a graphing utility to graph \(f\) and \(f^{\prime}\) on the interval \([-2,2]\). $$ f(x)=x^{2}(x+1)(x-1) $$
Find the derivative of the function. State which differentiation rule(s) you used to find the derivative. $$ f(x)=\frac{1}{\left(x^{2}-3 x\right)^{2}} $$
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