QUESTION 1

Find the area between the curves. 2x X: -1, x=3, y=2e2", y=e +1 The area between the curves is approximately (Do not round until the nal answer. Then round to the nearest hundredth as needed.) A company has found that the marginal cost (in thousands of dollars) to produce x central air conditioning units is 80): 5x2 +42 0'00 = , where x is the number of units produced. (a) Find the cost function, given that the company incurs a xed cost of $16,000 even if no units are built. (b) The company will seek a new source of investment income if the cost is more than $23,000 to produce 5 units. Should they seek this new source? (a) What substitution should be used to determine the cost function? Use the quantity V as the substitution, u = , so that du = E ) dx. The cost function is 000 = (b) Therefore. the cost of producing 5 units is $ so the company 7 seek a new source of investment income. (Round to the nearest dollar as needed.) Find all points where the function has any relative extrema. Identify any saddle points. f(x,y) = 2x2 + 3xy + 4y2 + 2x -10y Find all points where the function has relative maxima. Select the correct choice below and ll in any answer boxes within your choice. '3' A- The point(s) is(are) (Simplify your answer. Type an ordered pair. Use a comma to separate answers as needed.) (:2: B. There are no relative maxima. Find all points where the function has relative minima. Select the correct choice below and ll in any answer boxes within your choice. C? A- The point(s) is(are) (Simplify your answer. Type an ordered pair. Use a comma to separate answers as needed.) (:2- B. There are no local relative. Identify any saddle points. Select the correct choice below and ll in any answer boxes within your choice. [:3' A- There is(are) saddle point(s) located at (Simplify your answer. Type an ordered pair. Use a comma to separate answers as needed.) (:5 B. There are no saddle points. Find the area of the shaded region. The total area of the shaded regions is (Type an integer or a simplied fraction.)