9. [1/3 Points] DETAILS PREVIOUS ANSWERS HARMATHAP12 9.6.038. The revenue in dollars from the sale of x units of a product is represented by the following formula. (Round your answers to the nearest whole number.) R = 10(5x + 1)'1 + 80X 18 Find the marginal revenue when 30 units are sold. $:lx Interpret your result. If the sales go from 30 units sold to y units sold, the revenue will increase by about $ :] x Need Help? _' 10. [0/2 Points] DETAILS PREVIOUS ANSWERS HARMATHAP12 9.6.039. Suppose that the weekly sales volume y (in thousands of units sold) depends on the price per unit (in dollars) of the product according to the following formula. y = 31(3p + 1)'2/5, p > o (a) What is the rate of change in sales volume when the price is $20? (Round your answer to three decimal places.) (b) Interpret your answer to part (a). (Round your answer to the nearest whole number.) If the price increases $1, the sales volume will decrease by Z] X units. Need Help? _' 6. [-/1 Points] DETAILS HARMATHAP12 11.1.011. Find P if p = In(q8 + 3). dq dp = dq Need Help? Read It Watch It10. [0/2 Points] DETAILS PREVIOUS ANSWERS HARMATHAP12 9.5.022. For the function y = x - 3x at (1, - , find the following. (Give exact answers. Do not round.) x2 + 3x (a) the slope of the tangent line X (b) the instantaneous rate of change of the function Need Help? Read It Watch It Submit Answer 11. [-/1 Points] DETAILS HARMATHAP12 9.5.025. Write the equation of the tangent line to the graph of y = 6X" - 5x - 1 - at X = 1. Check the reasonableness of your answer by graphing both the function and the tangent line. 3 - x2 Need Help? Read It13. [-/2 Points] DETAILS HARMATHAP12 9.5.041.MI. Suppose the revenue (in dollars) from the sale of x units of a product is given by R(x) = 40x + 51x 2x + 2 Find the marginal revenue when 39 units are sold. (Round your answer to the nearest dollar.) LA Interpret your result. When 39 units are sold, the projected revenue from the sale of unit 40 would be $ Need Help? Read It Master It7. [-13 Points] DETAILS HARMATHAP12 9.9.020.M|. If the cost function for a commodity is C(X) = $9 + 6x2 + 6x + 12 dollars find the marginal cost W at x = 9 units. (Round your answer to two decimal places.) ~74: Tell what the marginal cost predicts about the cost of producing 1 additional unit. The cost of producing 1 additional unit is $ Z]. Tell what the marginal cost predicts about the cost of producing 2 additional units. The cost of producing 2 additional units is $ :| . Need Help? _' _' Submit Answer . [4I5 Points] DETAILS PREVIOUS ANSWERS HARMATHAP12 10.1.005. Use the sign diagram for f'(x) to determine the following. (If an answer does not exist, enter DNE.) f(x)0+++++0 |{_. x 6 9 Q) (a) the critical values of fIX) (Enter your answers as a comma-separated list.) X = 6,9 Exactly! y (b) intervals on which f(x) increases (Enter your answer using interval notation.) 6 9 Excellent! ( , V (c) intervals on which f(x) decreases (Enter your answer using interval notation.) (_ 0014) U (9100) X (d) x-values at which relative maxima occur (Enter your answers as a comma-separated list.) x = 9 Nice job! V (e) x-values at which relative minima occur (Enter your answers as a comma-separated list.) X = 6 That's great! V Need Help? 4. [1/3 Points] DETAILS PREVIOUS ANSWERS HARMATHAP12 10.1.009. Consider the following. y = 2x5 + 5x4 - 14 (a) Find the critical values of the function. (Enter your answers as a comma-separated list.) X = (-2,0) Amazing job. (b) Make a sign diagram and determine the relative maxima and minima. (If an answer does not exist, enter DNE.) relative maxima (x, y) = X relative minima (x, y) = X Need Help? Read It5. [-/8 Points] HARMATHAP12 10.1.015. MY NOTES Consider the following. 12 =x x y 2 (a) Find y' = m). f'(x) = (b) Find the critical value. x = (c) Find the critical point. MHZ) (d) Find intervals of x-values where the function is increasing. (Enter your answer using interval notation.) Find intervals of x-values where the function is decreasing. (Enter your answer using interval notation.) (e) Classify the critical point as a relative maximum, a relative minimum, or a horizontal point of inflection. In each case, check your conclusions with a graphing utility. (If an answer does not exist, enter DNE.) relative maxima (Xi Y) =( ) relative minima (X, Y) =( ) horizontal point of inection (x, y) =( ) Need Help? 6. [-/9 Points] DETAILS HARMATHAP12 10.1.017. MY NOTES Consider the following function. y = X + x2 - 2x + 6 3 (a) Find y' = f'(x). f' ( x ) = (b) Find the critical values. (Enter your answers as a comma-separated list.) X = (c) Find the critical points. ( x, y ) = ( (smaller x-value) ( x, y ) = ( (larger x-value) (d) Find intervals of x-values where the function is increasing. (Enter your answer using interval notation.) Find intervals of x-values where the function is decreasing. (Enter your answer using interval notation.) (e) Classify the critical points as relative maxima, relative minima, or horizontal points of inflection. In each case, check your conclusions with a graphing utility. (If an answer does not exist, enter DNE.) relative maxima ( x, y) =( relative minima ( x, y) =( horizontal points of inflection ( x, y ) =( Need Help? Read It3. [4/5 Points] PREVIOUS ANSWERS HARMATHAP1210.1.053.EP. Suppose that the average cost, in dollars, of producing a shipment of a certain product is 36,000 X E(x) = 4,000x + , x > 0 where x is the number of machines used in the production process. (a) Find Em. _ 2 36000 C'(x)= ( )( 2 ) >0 x X Given the domain ofx > 0, find the critical value of ax). x = 3 Nicejob! g/ The critical value is a \-/ (b) Over what interval does the average cost decrease? (Enter your answer using interval notation.) (0,3) Nice work! J (c) Over what interval does the average cost increase? (Enter your answer using interval notation.) (3,00) Outstanding! \/ Need Help? 9. [-13 Points] DETAILS HARMATHAP12 10.1.060.MI. The number of milligrams x of a medication in the bloodstream t hours after a dose is taken can be modeled by 50001' X(t) = . t2 + 25 (a) For what tvalues is x increasing? (Enter your answer using interval notation.) (b) Find the tvalue (in hr) at which x is maximum. (c) Find the maximum value ofx (in mg). "Em New Help? 4. [0/1 Points] DETAILS P Find the derivative of the function Y = 30(x