Calculus I

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1. Determine any absolute extrema over the given intervals:

a. b.

b. What if the interval in 2b is changed to ? Will the function have the same extrema? If so, at what values of x will the extrema occur?

2. Use Newton’s method to approximate the intersection of

3. Approximate by the indicated method:

a) using differentials

b) using Newton’s method

Which method produced a more accurate approximation ?

4. The circumference of a circle is measured to be 16 inches with a possible error of

+1/2 inch.

a) Determine the area of the circle

b) Determine the maximum possible error in the calculated value of the area

c) Determine the percentage error in the measurement of the circumference and the

calculation of the area.

5. An open rectangular box is to hold 108 in3. The base of the box is rectangular with it length 4

times the width. If the material for the base is $4/in2 and the material for the sides cost

$3/in2, determine the dimensions of least cost.

6. A university is trying to determine what price to charge for tickets to football games.

At a price of $18 per ticket, attendance averages 40,000 people per game. Every

decrease of $3 adds 10,000 people to the average number. Every person at the game

spends an average of $4.50 on concessions.

a) What price per ticket should be charged to maximize the revenue?

b) How many people will attend at that price?

c) What is the maximum revenue per game?

To answer the questions sub in the value of t at w (number of watcher) and p (price of ticket).

7. The radius of a sphere is measured with a possible error of +2%. Determine the

maximum possible errors in the calculation of the surface area and the volume.

8. Twenty feet of wire can be bent into a rectangle with a length twice the width, an

equilateral triangle or be cut and used for both figures. How much wire should be used

for both figures to enclose:

a) The greatest area

b) The least area

9. Verify the hypotheses of the Mean Value theorem are satisfied on the given interval and

determine the value of c that satisfies the conclusion of the theorem.

10. Let

Does the function satisfy the hypotheses of Rolle’s theorem? If so, find the value of c that

satisfies the conclusion of the theorem. If not, explain why.