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 inter
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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 inter
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 postive values of a since this represents items produced and sold. Explain how these answers relate to your work with the marginal functions by filling in the blanks.
Interval(s) on which P'(x) > 0: On this interval(s), the profit funciton P(x) is (increasing or decreasing) Interval(s) on which P'(x) < 0: On this interval(s), the profit funciton P(x) is. (increasing or decreasing) Comparing my answers with #4 and #5 above, I see that: • P'(x) > 0 when marginal cost is ● less) than marginal revenue. On this interval(s), profit is (increasing or decreasing). P'(x) < 0 when marginal cost is (greater or (greater or
12. Fill in the sign chart for P'(r) 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 P' above the appropriate intervals on the number line, and finally type either increasing or decreasing next to each "P is" below the appropriate intervals on the number line. Then fill in the blanks to determine if this monopoly has a maximum or minimum profit.
P' 0 Pis This monopoly has a of items. c.n. = P' P is (maximum or minimum) profit (include units) when they produce and sell
- C/Users/ctind/Downloads/%20Tindall%20Chad.pdf AN I A monopolist's cost function is C(r) 2500 for z items produced. Their price (or demand) function is given by p(x) = 20 hundred dollars for z items sold. MC(x) = C'(x) = 7 29 (z-100)2 +z hundred dollars a 25 1. In the CAS Perspective, type C(x):=(x/2500)*(x-100)^2 + x (the cost function) on an empty Input line and hit enter. On the In- put line below, find the derivative of C(z) by either typing C'(x) or Derivative (C(x)). This is the marginal cost function. Write it below exactly as it appears in the CAS panel. 1/2500(3^x2-400x+12500) 2. Find the the company's revenue function. In the CAS Perspective, type: p(x): 20 x/25 on an empty Input line. On the line below, type R(x):=x* p(x). This will be your revenue function. Write it below exactly as it appears in the CAS panel. 36 33 15
I 2500 A monopolist's cost function is C(x) = (x-100)2 + z hundred dollars for x items produced. Their price (or demand) function is given by p(x)=20- hundred dollars for r items sold. 25 1. In the CAS Perspective, type C(x):=(x/2500)*(x-100)^2 + x (the cost function) on an empty Input line and hit enter. On the In- put line below, find the derivative of C(z) by either typing C'(x) or Derivative (C(x)). This is the marginal cost function. Write it below exactly as it appears in the CAS panel. MC(x) = C'(x) = 1/2500(3^x2-400x+12500) 2. Find the the company's revenue function. In the CAS Perspective, type p(x): 20 x/25 on an empty Input line. On the line below, type R(x):= x p(x). This will be your revenue function. Write it below exactly as it appears in the CAS panel. *