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Chapter 7: Problem 25
Use the General Power Rule to find the derivative of the function. $$ g(x)=(4-2 x)^{3} $$
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Use the General Power Rule to find the derivative of the function. $$ y=\sqrt[3]{9 x^{2}+4} $$
The cost of producing \(x\) units of a product is given by \(C=x^{3}-15 x^{2}+87 x-73, \quad 4 \leq x \leq 9\) (a) Use a graphing utility to graph the marginal cost function and the average cost function, \(C / x\), in the same viewing window. (b) Find the point of intersection of the graphs of \(d C / d x\) and \(C / x\). Does this point have any significance?
Find the derivative of the function. State which differentiation rule(s) you used to find the derivative. $$ g(s)=\frac{s^{2}-2 s+5}{\sqrt{s}} $$
The monthly sales of memberships \(M\) at a newly built fitness center are modeled by \(M(t)=\frac{300 t}{t^{2}+1}+8\) where \(t\) is the number of months since the center opened. (a) Find \(M^{\prime}(t)\). (b) Find \(M(3)\) and \(M^{\prime}(3)\) and interpret the results. (c) Find \(M(24)\) and \(M^{\prime}(24)\) and interpret the results.
You deposit in an account with an annual interest rate of \(r\) (in decimal form) compounded monthly. At the end of 5 years, the balance is \(A=1000\left(1+\frac{r}{12}\right)^{60}\) Find the rates of change of \(A\) with respect to \(r\) when (a) \(r=0.08\), (b) \(r=0.10\), and (c) \(r=0.12\).
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