Exam 4: Applications of Differentiation

Select the correct Answer for each question. -The function satisfies the hypotheses of the Mean Value Theorem on the interval Find all values of c that satisfy the conclusion of the theorem.

a) Graph the funtion b) Use l'Hos pitals' rule to explain the behavior as

Find the intervals where is increasing and where it is decreasing.

A production editor decided that a promotional flyer should have a argin at the top and the bottom, and a margin on each side.The editor further stipulated that the flyer should have an area of 72 Determine the dimensions of the flyer that will result in the maximum printed area on the flyer.Select the correct Answer

What can you say about point of inflation for ?

Determine where the graph of is concave upward and where it is concave downward.Also, find all inflection points of the function.

Select the correct Answer for each question. -Find the value of the limit.

Select the correct Answer for each question. -The function satisfies the hypotheses of Rolle's Theorem on the interval Find all values of c that satisfy the conclusion of the theorem.

Evaluate the limit.

Find the inflection points for the function given.Select the correct Answer

Select the correct Answer for each question. -Verify that the function satisfies the three hypotheses of Rolle's Theorem on the given interval.Then find all numbers c that satisfy the conclusion of Rolle's Theorem.

A rectangular beam will be cut from a cylindrical log of radius inches.Suppose that the strength of a rectangular beam is proportional to the product of its width and the square of its depth.Find the dimensions of the strongest beam that can be cut from the cylindrical log.

Sketch the graph of the function on using the curve-sketching guidelines.

Sketch the graph of the function using the curve-sketching guidelines.

Find the critical number(s), if any, of the function

A skydiver leaps from a helicopter hovering high above the ground.Her velocity t sec later and before deploying her parachute is given by where is measured in meters per second.What is her terminal velocity? Hint: Evaluate

The graph of the derivative of a continuous function f is shown.On what intervals is decreasing? .

Given (a) Find the intervals on which is increasing or decreasing.(b) Find the relative maxima and relative minima of

An apple orchard has an average yield of 32 bushels of apples per tree if tree density is 30 trees per acre.For each unit increase in tree density, the yield decreases by 2 bushels per tree.How many trees per acre should be planted to maximize yield? Select the correct Answer