EXERCISE SET 2: Answer the following questions. It may a good

idea to start a new GeoGebra le at this point since we will be

using the same function letters for cost, revenue, and prot as we

did in the rst Exercise Set. We will continue to work in the CAS

Perspective.

A monopolist's cost function is C(x) = (x/2500)(x-100)^2+x hundred dollars

for x items produced. Their price (or demand) function is given by

p(x) = 20- (x/25) hundred dollars for x items sold.

10. Recall that local extreme values of a function can occur only at the crit-

ical numbers of the function (domain values at which the derivative is

equal to zero). Find the positive critical numbers of P(x) by typing

Solve(P'(x)=0) in the CAS Perspective. Write your answer(s) in the

space provided. Explain how these answers relate to your work with the

marginal functions. Recall we are only considering x greater than and equal to 0.

Critical Number(s) of P(x): x = items

Type a sentence or two explaining how your answer here relates to

your answers above with the marginal functions. Look at your answer

for #6.

(6. If profit is to be maximized, it occurs when the marginal cost equals

marginal revenue. Determine the number of items produced and sold

for which the marginal functions agree. In the CAS Perspective, type

Solve(R'(x)=C'(x)). Write your answers below. Again, consider only

X greater than and equal to 0.

C(x) = R(x) when x = 150 items)

11. Recall that if f(x) > 0 on an interval I, then f(x) increases on the

interval I. Similarly if f(x) < 0 on an interval I, then f(x) decreases

on the interval I. Because the sign of the derivative tells us where

functions increase and decrease, we use the sign of the derivative to

determine if the critical numbers give us a relative maximum or relative

minimum (or neither) value of f(x). Working in the CAS Perspective

type Solve(P'(x)>0) and Solve(P'(x)<0) (of course, this should be

done on two separate input lines). Write your answers below in interval

notation. Remember we are only considering positive values of x since

This represents items produced and sold. Explain how these answers

relate to your work with the marginal functions by lling in the blanks.

Interval(s) on which P(x) > 0:

On this interval(s), the profit function P(x) is (increasing or decreasing)

Interval(s) on which P(x) < 0:

On this interval(s), the profit function P(x) is (increasing or decreasing)

Comparing my answers with #4 and #5 above, I see that:

P(x) > 0 when marginal cost is (greater or less) than marginal revenue. On this interval(s), profit is (increasing or decreasing).

P(x) < 0 when marginal cost is (greater or less) than marginal revenue. On this interval(s), profit is (increasing or decreasing).

12. Fill in the sign chart for P0(x) below. Type your critical number under

the hash mark on the number line next to \c.n. = " . The type either

\> 0 " or \< 0" next to each P0 above the appropriate intervals on the

number line, and nally type either increasing or decreasing next to each

\P is" below the appropriate intervals on the number line. Then ll in

the blanks to determine if this monopoly has a maximum or minimum

Profit

This monopoly has a (maximum or minimum) profit

Of (include units) when they produce and sell items.

what other info do u need ? that is straight from my lab