37. DETAILS Derivatives. If f(x) = 2 + 4x2 + e3*, then f(3)(x) is equal to: O 8x2 + 93x O ge 3x O 8 x2 + 3e3X O 8x + 303x O 27e 3x O 8x + ge3x O 81e3x O None of the other answers OO O 3-3x38. DETAILS MY NOTES | ASK YOUR TEACHEF ............................................................................................................................................................................................................................................... Bicycles. A local company that manufactures and sells bikes has found that its monthly revenue (in dollars) is given by R(x,y) = 5 x2 2.5 y2 5 xy + 600 x + 320 y where X is the number of mountain bikes and y is the number of city bikes that it sells each month. (a) The critical point of R(x,y) is 0 (8,56) 0 (56,8) 0 (40,60) 0 (60,40) 0 (90,15) 0 (15,90) 0 There is no critical point 0 (0,0) (b) Let D(x,y)=Rxx(x,y)Ryy(x,y}ny2(x,y). Suppose that a is the number of mountain bikes and b is the number of city bikes that should be sold each month to ensure a maximum monthly revenue. Which of the following statements is true? 0 D(a,b) > 0 and Rxx(a,b) 0 and Rxx(a,b) > 0 O D(a,b) = 0 O D(a,b) 0 39. DETAILS Derivative. The derivative of e -4 h ( x) =- 2 + e (4 x + 8 ) is Oh' ( x ) = - e ( 4x2+ 8) (8x) (2 + e ( 4 x2 + 8 ) , 2 Oh' ( x ) = e-4 ( - 4) (2 + e ( 4x 2 + 8) )-e (4x2 + 8) (8x) (e-4) ( 2 + e ( 4 * 2 + 8 ) ) 2 O none of the other answers Oh' ( x ) = - e ( 4x2 + 8) (8x) (e-4) ( 2 + e ( 4 x 2 + 8 ) , 2 O h'( x ) = e-4 ( - 4) (2 + e (4x2 + 8 ) )-e(4x2 + 8) (8x) (e-4) (2 + e ( 4 x2 + 8 ) )Fencing. A fence is to be built around a rectangular area of 14 square metres. The dimensions are x and y. On one of the sides with length X, there is a gap of 0.5x that has no fence. The goal is to find the dimensions for the minimum fence length. (a) The length equation can be expressed as O L(x)=14+2x O L(x)=2x+ X 0 L(x)=1.5x+ X 0 L(x)=1.5x+ X 0 L(x)= 1.5X+ X2 (b) The length X for the minimum fence length is 0 1.8001 m 0 4.1572 m 0 2.9396 m 0 None of the other answers 0 4.3205 m Submit