Exam 6: Applications of Differentiation

Determine whether the Mean Value Theorem can be applied to the function on the closed interval [5,15]. If the Mean Value Theorem can be applied, find all numbers c in the open interval (5,15) such that .

Find the value of the derivative (if it exists) of at the indicated extremum.

The total stopping distance T of a vehicle is where T is in feet and x is the speed in miles per hour. Use differentials to approximate the percent change in total stopping distance as speed changes from x = 30 to x = 35 miles per hour. Round your answer to one decimal place.

Determine whether the Mean Value Theorem can be applied to the function on the closed interval [0,14]. If the Mean Value Theorem can be applied, find all numbers c in the open interval (0,14) such that .

Locate the absolute extrema of the function on the closed interval .

Find the limit.

Find two positive numbers whose product is 190 and whose sum is a minimum.

The radius of a spherical balloon is measured to be 7 inches, with a possible error of 0.06 inch. Use differentials to approximate the maximum possible error in calculating the volume of the sphere. Round your answer to two decimal places.

The graph of a function f is is shown below. Sketch the graph of the derivative .

Match the function with one of the following graphs.

The graph of f is shown. Graph f, f' and f'' on the same set of coordinate axes.

Sketch the graph of the function using any extrema, intercepts, symmetry, and asymptotes.

Compare dy and for at x = -1 with dx = -0.07. Give your answers to four decimal places.

Find the length and width of a rectangle that has perimeter meters and a maximum area.

The height of an object t seconds after it is dropped from a height of 250 meters is Find the average velocity of the object during the first 10 seconds.

Locate the absolute extrema of the function on the closed interval .

Suppose the total cost C for ordering and storing x units is What order size will produce a minimum cost? Round your answer to the nearest unit produced.

The graph of f is shown in the figure. Sketch a graph of the derivative of f.

Use the graph of the function given below to estimate the open intervals on which the function is increasing or decreasing.

Analyze and sketch a graph of the function .