12.4 Derivatives  (Page 10/18)

$f(0)=600$

$f\text{'}(30)=\mathrm{-20}$

$f(30)=0$

$f\text{'}(200)=30$

$f(240)=500$

$s(2)=96$

$s\text{'}(2)=16$

$s(3)=96$

$s\text{'}(3)=\mathrm{-16}$

$s(0)=0,s(5)=0.$

Find the average rate of change of $V$ as $r$ changes from 1 cm to 2 cm.

Find the instantaneous rate of change of $V$ when $r=3\text{ cm}\text{.}$

Find the average change of the revenue function as $x$ changes from $x=10$ to $x=20.$

Find $R\text{'}(10)$ and interpret.

Find $R\text{'}(15)$ and interpret. Compare $R\text{'}(15)$ to $R\text{'}(10),$ and explain the difference.

Find the average rate of change in the total cost as $x$ changes from $x=10\text{ to }x=15.$

Find the approximate marginal cost, when 15 cellphones have been produced, of producing the 16 ^th cellphone.

Find the approximate marginal cost, when 20 cellphones have been produced, of producing the 21 ^st cellphone.

$f(x)=\frac{1}{x^2}$

$f(x)=5x^2-x+4$

$f(x)=-x^2+4x+7$

$f(x)=\frac{-4}{3-x^2}$

$\underset{x\to {\mathrm{-1}}^{+}}{\lim }f(x)$

$\underset{x\to {\mathrm{-1}}^{-}}{\lim }f(x)$

$\underset{x\to -1}{\lim }f(x)$

$\underset{x\to 3}{\lim }f(x)$

At what values of $x$ is the function discontinuous? What condition of continuity is violated?

Using [link] , estimate $\underset{x\to 0}{\lim }f(x).$

$f(x)=\{\begin{array}{lll}\left|x\right|-1,\hfill & if\hfill & x\ne 1\hfill \\ x^3,\hfill & if\hfill & x=1\hfill \end{array}a=1$

$f(x)=\{\begin{array}{lll}\frac{1}{x+1},\hfill & if\hfill & x=-2\hfill \\ {(x+1)}^2,\hfill & if\hfill & x\ne -2\hfill \end{array}a=-2$

$f(x)=\{\begin{array}{lll}\sqrt{x+3},\hfill & if\hfill & x<1\hfill \\ -\sqrt[3]{x},\hfill & if\hfill & x>1\hfill \end{array}a=1$