91Ó°ÊÓ

Marginal Revenue The revenue \(R\) (in dollars) from renting \(x\) apartments can be modeled by \(R=2 x\left(900+32 x-x^{2}\right)\) (a) Find the additional revenue when the number of rentals (a) Find the additional revenue when the number of rentals is increased from 14 to 15 . (b) Find the marginal revenue when \(x=14\). (c) Compare the results of parts (a) and (b).

Find the derivative of the function. State which differentiation rule(s) you used to find the derivative, $$ f(x)=\frac{x^{3}+3 x+2}{x^{2}-1} $$

Use the limit definition to find the derivative of the function. $$ f(x)=1-x^{2} $$

Find the value of the derivative of the function at the given point. $$ {y=3 x\left(x^{2}-\frac{2}{x}\right)} \quad (2,18) $$

Use the General Power Rule to find the derivative of the function. $$ g(x)=\sqrt{5-3 x} $$

Marginal Profit The profit \(P\) (in dollars) from selling \(x\) units of calculus textbooks is given by \(P=-0.05 x^{2}+20 x-1000\) (a) Find the additional profit when the sales increase from 150 to 151 units. (b) Find the marginal profit when \(x=150\). (c) Compare the results of parts (a) and (b).

Use the General Power Rule to find the derivative of the function. $$ s(t)=\sqrt{2 t^{2}+5 t+2} $$

Use the limit definition to find the derivative of the function. $$ h(t)=\sqrt{t-1} $$

Find the value of the derivative of the function at the given point. $$ y=(2 x+1)^{2} \quad(0,1) $$

Find the derivative of the function. State which differentiation rule(s) you used to find the derivative, $$ f(x)=\frac{3-2 x-x^{2}}{x^{2}-1} $$