Exam 4: Applications of the Derivative

If the concentration of a chemical changes according to the equation , find the concentration for which the reaction rate is a maximum. Round answer to nearest hundredth.

Determine, by hand, all critical numbers of and use the First Derivative Test to classify each as a local minimum, local maximum or neither.

Estimate the intervals where the function shown below is concave up and/or concave down.

A herd of ninety-nine antelope is released onto a small game reserve so that their reproductive habits can be studied. In the beginning the population of the herd increases rapidly in size but eventually slows due to a dwindling food supply. Suppose the population of antelope after t years is given by the function where . Determine when the population begins to decline.

Suppose a snowball melts in such a way that it maintains a spherical shape. If the radius is decreasing at a rate of 0.75 cm per hour when the radius is 10 cm, how fast is the volume of the snowball decreasing at that instant?

Using Newton's method, approximate the root of the following equation to at least six-digit accuracy. x³ + x² - 3x + 5 = 0

Sketch a graph of a function with the following properties. if if

Given the graph of , locate the absolute extrema (if they exist) on the interval .

Find (by hand) all critical numbers and use the First Derivative Test to classify each as the location of a local maximum, local minimum or neither. y = x^4/3 - 8x^1/3 - 6

Given determine if the critical number represents a local maximum, local minimum or neither.

A certain company estimates that it can sell f(x)-thousand video game consoles at the price of $x as given in the table. Use a linear approximation to estimate the number of consoles that can be sold at $62.

Find the absolute extrema of the given function on the indicated interval. on

Given , on the interval , determine if the critical number represents a local maximum, local minimum or neither.

Find all critical numbers by hand. f (x) = x^4/3 + 4x^1/3 + 24x^-2/3

Graph the function and completely discuss the graph.

Determine, by hand, all critical numbers of and use the First Derivative Test to classify each as a local minimum, local maximum or neither.

Given the graph of , locate the absolute extrema (if they exist) on the interval .

Suppose that at the price dollars the demand for a product is inelastic. If the price is increased, what will happen to revenue?