An individuals utility function is given by U = 900x₁ + 500x₂ + 6x₁x2 − x² − x²/2, when the weekly amount of leisure is X1 = 140 and earned income is x₂ = 800 answer the following: 1. The marginal utility of ₁ is 2. The marginal utility of 2 is 3. Use the small increments formula to estimate the change in the utility when ₁ decreases by 1 and 2 increases by 4. The change - 4. Does the law of diminishing marginal utility hold? 5. The MRCS at a given values is Enter non-integer numerical values as decimals to at least 3 decimal places. Note: you must use a . and not, for a decimal point.

The U.S. population can be modeled by the function y=165.6x¹.345, where y is in thousands and x is the number of years after 1800. (a) What was the population in 1970, according to this model? (b) is the graph of this function concave up or concave down? What does this mean? (c) Use numerical or graphical methods to find when the model estimates the population was 94,150,000. (a) According to the model, the population in 1970 was thousands. (Round to the nearest integer as needed.)

1024 If the price of a product is given by P(x) = - + 2,300, where x represents the demand for the product, find the rate of change of price when the demand is 8. X @ 2 OA. - 138 OB. -16 OC. 138 OD. 16 N F2 W S 20 #3 X SP F6 NOV 27 command F3 E D 000 54 $ C F4 R 70 FL % 5 V F5 T G A 6 VISSA B F6 Y & 7 H F7 U N 8 J ♫ F8 I M - O 9 #tv A ▶ K F9 O < H 0 L 4 F10 P II ; 4) F11 alt { [ command option + 11 = ? I O 4))) F12 Submit Next } 1 U dele .

1. A tennis ball is dropped from the top of a building that is 1545 feet tall, with an initial velocity of -30.5 feet per second. Use the position function s(t)=-16t^2+v0t+s0 to help you answer the given questions. a.Write the equations of the position and instantaneous velocity functions. b. What is the average velocity over the first two seconds? c.When does the coin hit the ground? Round your answer to two decimal places. d.What is the velocity of the coin upon impact? 2.find all the values of x for which f(x) will have a horizontal tangent line f(x)=(x-4)/(x^2-7) 3. Find the derivative of the function. g(x)=4x(3x+2)^5 4.