A note card company has found that the marginal cost per card of producing x note cards is given by the function below, where C'(x) is the marginal cost, in cents, per card. Find the total cost 0' producing 580 cards, disregarding any xed costs. C'(X) = - 0.05x+ 75, for X5 1000 The total cost is cents Find s(t), where s(t) represents the position function, v(t) represents the velocity function, and a(t) represents the acceleration function. a(t) = 241 + a, with v(0) = 4 and s(O) =1 s(t) Find the area under the graph offover the interval [- 2,5]. 2 x53 f(x)= x +3 4x x>3 The area is . (Simplify your answer.) Find the area of the region bounded by the graphs of the given equations. y=3,y=i/I,x=o The area of the region is . (Simplify your answer.) -2000x Arm has the marginal-demand function D'(x) = 2, where D(x) is the number of units sold at x dollars per unit. Find the demand function given that D = 16,000 when X: $3 per unit. 25-x The demand function is D(x) = D. Consider the graph to the right. Explain the idea of a critical value. Then determine which xvalues are critical values, and state why. .\\'1 .\\'2 X3 X4 X1 ".0"..- .\\'8.\\'0 X] What is the idea of a critical value? Critical values are yvalues where relative extrema may occur. Critical values are xvalues where relative extrema may occur. Critical values are the yvalues of relative extrema. Critical values are xvalues where relative extrema occur. Which xvalues are critical values? x4 and x7 because a corner exists at these xvalues. x1 , x3, x5, x6, x8, and x10 because relative extrema occur at these points. '2: _:- C. All x-values are critical values because they all occur at relative extrema or where the slopes of the tangent lines do not exist. .;_ _:- D. x1,x3,x4,x5, x6, x7, x8, and x10 because the slopes of the tangent lines at these points are 0 or do not occur. According to a study, a vehicle's fuel economy, in miles per gallon (mpg), decreases rapidly for speeds over 60 mph. a) Estimate the speed at which the absolute maximum gasoline mileage is obtained. b) Estimate the speed at which the absolute minimum gasoline mileage is obtained. c) What is the mileage obtained at 70 mph? a) The speed at which the absolute maximum gasoline mileage is obtained is approximately V (Type a whole number.) b) The speed at which the absolute minimum gasoline mileage is obtained is approximately V (Type a whole number.) c) The mileage obtained at 70 mph is D V (Type a whole number.) Fuel economy (mpg) 36 30 24 18 12 5 15 25 35 45 55 65 75 85 95 Speed (mph) > 99 E