Find the indicated derivative for each function.

$h''(x)$ for $h(x)=2x^{-1}-3x^{-2}$

An efficiency study conducted for Elektra Electronics showed that the number of Space Commander walkie-talkies assembled by the average worker during the morning shift thr after starting work at 8 A.M. is given by $N ( t ) = - t ^ { 3 } + 6 t ^ { 2 } + 15 t \quad ( 0 \leq t \leq 4 )$

At what rate will the average worker be assembling walkie-talkies at 10 A.M.? At 11 A.M.?

An efficiency study conducted for Elektra Electronics showed that the number of Space Commander walkie-talkies assembled by the average worker $t$ hr after starting work at 8 a.m. is given by

$$N(t)= -t^3 + 6t^2 + 15t \quad (0 \le t \le 4)$$

At what time during the morning shift is the average worker performing at peak efficiency?

An efficiency study conducted for Elektra Electronics showed that the number of Space Commander walkie-talkies assembled by the average worker during the morning shift thr after starting work at 8 A.M. is given by $N ( t ) = - t ^ { 3 } + 6 t ^ { 2 } + 15 t \quad ( 0 \leq t \leq 4 )$

Find the rate at which the average worker will be assembling walkie-talkies thr after starting work.

The demand function for Sportsman $5 \times 7$ tents is given by $p=f(x)=-0.1 x^{2}-x+40$ where p is measured in dollars and x is measured in units of a thousand.

What is the rate of change of the unit price if the quantity demanded is 5000?

The demand function for Sportsman $5 \times 7$ tents is given by $p=f(x)=-0.1 x^{2}-x+40$ where p is measured in dollars and x is measured in units of a thousand.

Find the average rate of change in the unit price of a tent if the quantity demanded is between 5000 and 5050 tents; between 5000 and 5010 tents.

$$\begin{array} { l } { \text { Find the second derivative } d ^ { 2 } y / d x ^ { 2 } \text { of the } } \\ { \text { function defined implicitly by the equation. } } \end{array}$$

$$x ^ { 1 / 3 } + y ^ { 1 / 3 } = 1$$

$$\begin{array} { l } { \text { Find the second derivative } d ^ { 2 } y / d x ^ { 2 } \text { of the } } \\ { \text { function defined implicitly by the equation. } } \end{array}$$

$$x y = 1$$

$$\begin{array} { l } { \text { Find the second derivative } d ^ { 2 } y / d x ^ { 2 } \text { of the } } \\ { \text { function defined implicitly by the equation. } } \end{array}$$

$$y ^ { 2 } - x y = 8$$

$$\begin{array} { l } { \text { Find the second derivative } d ^ { 2 } y / d x ^ { 2 } \text { of the } } \\ { \text { function defined implicitly by the equation. } } \end{array}$$

$$x ^ { 3 } + y ^ { 3 } = 28$$

Find the absolute maximum and absolute minimum of each function on the indicated intervals.

$$f(x)=2x-5$$

$$(A)\ [0,4]\qquad (B)\ [0,10]\qquad (C)[-5,10]$$

Find the indicated derivative for each function.

$g''(x)$ for $g(x)=-x^{3}+2x^{2}-3x+9$

Find the $x$ and $y$ coordinates of all inflection points.

$$f(x)=x^{4}-16x^{3}+10$$

Express the given quantity as a function $f(x)$ of one variable $x$.

Find the dimensions of a rectangle with a perimeter of $76$ feet that has the maximum area.