Exam 4: Applications of Differentiation

Find all the critical numbers of the function.

The altitude (in feet) attained by a model rocket t sec into flight is given by the function When is the rocket ascending, and when is it descending? What is the maximum altitude attained by the rocket?

What is the shortest possible length of the line segment that is cut off by the first quadrant and is tangent to the curve at some point? Select the correct Answer

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

Sketch the curve.

A tall runs parallel to a tall building at a distance of from the building.What is the length of the shortest ladder that will reach from the ground over the fence to the wall of the building? Round the result to the nearest hundredth.

Evaluate the limit using l'Hôpital's Rule.Select the correct Answer

Estimate the extreme values of the function.

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

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

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

The owner of a ranch has 1,800 yd of fencing with which to enclose a rectangular piece of grazing land situated along a straight portion of a river.If fencing is not required along the river, what are the dimensions of the largest area he can enclose? What is the area?

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

How many points of inflection are on the graph of the function?

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

Use Newton's method to approximate the zero of between and using Continue until two successive approximations differ by less than 0.00001.

Evaluate and tell whether its antiderivative is increasing or decreasing at the point radians.

Find Select the correct Answer

The average cost of producing x units of a commodity is given by the equation Find the marginal cost at a production level of 1,255 units.

Find the maximum and minimum points of the function.