Question:
$ 5(NC). A balloonist drops a sandbag om a balloon 160 feet above the ground. After 1 seconds, the sandbag is 160 i6t2feet above the ground. With what velocity does the sandbag strike the ground? (A)32J (3)325 (Chm/To (Db/E (E)16 3.2 Definition of Derivative. Differentiability. NCl) The number of ducks in a pond x hours after 3 :00 PM is given by 1/11. At what rate 3: are the ducks leaving the pond at 6:00 PM, in ducks per hour? 1 (A>$(B)(c>35(D)}(E) 2 NC2) For the function represented by y = 21% for positive x and y and constants a a and I), what is the slope of the tangent line at point P [mg] ? 4 4 4 4 (A)E(B)E(C)4ab(D);(E); NC3) The smell of pizza in a kitchen diffuses outward in concentric circles. If, after t minutes, the radius of the smell is St meters, What is the rate of change of the area of the smell when the smell reaches Joe, who is 10 meters away? (A) 507: (3)10 (C) 5 (0)2007: (E) 100;; NC4) The graph of f '(x) on the interval [-4,4] is shown below. When x = 1,f (x) is equal to 3. What is the equation of the line tangent to the graph 0ff(x) atx = -1? 2.3 Techniques of differentiation NCl. A normal line to the graph of a function f at point (x, f (x)) is the line perpendicular to the tangent line at that same point. An equation of the normal line to the curve y = X2 +x at the point Wherex=1is (A) 3y+x=7 (B) 3y+x=2 (c) 3yx=2 (D) 3y+x:13 (E)y-3x='7 NCZ. The position of an object at time t is described by the function 3(1'): #(t2 22' + 4) (t3 2t). What is the velocity ofthe object when 1' =1? -2 be Dz. ,_t ('3 m t: Vvv do 4x2 3x+79 5x . NC3. What is the derivative of: 4362 +7 NC4. Let f (t) = tizl For what value of t is f ' (t) equal to the average rate of change of f on the closed interval [a,b]? 22 22 22 ab 2511b (C)32ab (A) 3(a_b) (B) 3(a_b) (D) \"1:613 (E) (:5) Mathboat.com NC5. If f' (x) = lim ( xth ) - (x2 ) what is the equation h of the line tangent to the curve y = f (x) at the point (3,9)? 23 (A) y= 6x -9 (By = 6x -27 (C) y-9=--(x-3) (D) y- 9=4(x-3) (Ey = 3x +9 1:3Mathboat.com 2.4 Derivatives of trig functions. Trigonometric Limits. Cl. The function f (x) = sin2 x - cosxsin|~ is given on the interval (0, 5). Approximately at which x-coordinates is f not differentiable? (A) {0, 3.7} (B) (0.9, 2.4, 3.7) (C) {0.4, 1.7, 3.1, 4.5} (D) (2.4, 4.5) ( E) {0.9, 1.7, 4.5} NC2. Which of the following is an equation of the normal line to the 1- cos x graph of y = at point P 1 + cos x ( A) y-1 = -- x- 2 25 (B ) y - 1 = 2 x-2 (C) y - 1=~ x -2 (D) y- 1= - 2 x-2 ( E) y-1= , (14)
