The energy cost of horizontal locomotion as a function of the body weight of a marsupial is given by

$$E=22.8 w^{-11,34} .$$

where $w$ is the weight of the animal (in $\mathrm{kg}$ ) and $E$ is the energy expenditure (in $\mathrm{kcal} / \mathrm{kg} / \mathrm{km}$ ). Source: Wildlife Feeding and Nutrition. Suppose that the weight of a 10-kg marsupial is increasing at a rate of $0.1 \mathrm{~kg} / \mathrm{day}$. Find the rate at which the energy expenditure is changing with respect to time.

Cells in the human body are not necessarily spherical; some cancer cells are cylindrical. Source: American Journal of Surgical Pathology. Suppose that the volume of such a cell is $65 \mu \mathrm{m}^3$. Find the radius and height of the cell with the minimum surface area.

Find the absolute maximum and minimum of $f(x) = \dfrac{2 \ln x}{x^2}$ on each interval. (a) [1, 4] (b) [2, 5]

Find $d y / d x$ by implicit differentiation for the following.\

$$\sin (x y)=x$$

The energy cost of horizontal locomotion as a function of the body mass of a lizard is given by $E = 26.5m^{-0.34}$, where $m$ is the mass of the lizard (in kilograms) and $E$ is the energy expenditure (in kcal/kg/km). Suppose that the mass of a 5-kg lizard is increasing at a rate of 0.05 kg per day. Find the rate at which the energy expenditure is changing with respect to time.

The average daily metabolic rate for captive animals from weasels to elk can be expressed as a function of mass by $r = 140.2m^{0.75}$, where $m$ is the mass of the animal (in kilograms) and $r$ is the metabolic rate (in kcal per day). (a) Suppose that the mass of a weasel is changing with respect to time at a rate $dm/dt$. Find $dr/dt$. (b) Determine $dr/dt$ for a 250-kg elk that is gaining mass at a rate of 2 kg per day.