Question 4 2 pts When simplified, which of the following is NOT the implicit derivative of the equation 3y" + 3xy + 4x = 0 ? a. -4-3y 3x+9y2 b. -3y+4 9y2+3x 4+3y C. 3x+9y2 d. 3y+4 9y2+3x Ob OC O d Question 5 2 pts What is the slope of a line tangent to the curve 3y' + 3xy + 4x = 0 at P(0,1)? O 11/17 O 8/17 O -7/9 O -5/9 Question 6 2 pts If the given equation is x - 2xy + x y + y = 10, which of the following is correct about the solution? a. (x - 2xy + x2y + y) = 10 b. a (x) - dx ( 2xy ) + (x2y ) + + (1 ) = (10) Ob O both a and b O neither a nor b Question 7 2 pts If the given equation is x - 2xy +x y + y = 10, which of the following is correct about the solution when implicit differentiation is applied? a. 1-2+ at 2y + 2x dx raytytax dy = 0 b. 1 - y(2) ax 2) dy + x2 (1) + y(2x) 2 + c. 1 - 2x(1) ~ + y(-2) dy+. Pax + x2 (1) dy + " + y (2x) + ax d. 1 - 2x(1) + y(-2) + x2 (1) + y(2x) + =0D Question 8 2 pts Based on your answer in Question no. 8, which of the following solutions is correct? a. (-2x + x2 + 1) = -1+2y -2xy b. " (-2x - 2y + x21) = -1 -2xy C. "(2y + 2xy) = 2 - x2 d. " (-2x + x2) = -1 -x2 + 2y -2xy O a Ob O c Od D Question 9 2 pts When simplified, which of the following is the implicit derivative of the equation x - 2xy +x y + y = 10? a. x2-2x+2y x-2xy-1 b. x2-2x+1 2y-2xy-1 C. 2y-2xy-1 x2-2x+1 d. zy-x2-2xy-1 x2-2x O a O c O d D Question 10 2 pts What is the slope of a line tangent to the curve x - 2xy +x y + y = 10 at P(-2,3)? O 17/9 O 15/8 O 13/7 O 11/6 D Question 11 2 pts Which of the following is the second derivative of f(a) = 3ac - 4x3 + 2x2 - 9? dry a. dx2 7 = 360x b. day dx2 = 180x2 - 24 C. 72 = 60x3 - 24x + 4 d. day dx2 = 15x* - 12x2 + 4x - 9Question 1 2 pts If the given equation is 3y3 + 3333; + 4a: = 0 and the rst step in applying implicit differentiation is to differentiate both sides of the equation with respect to x, which of the following is/are NOT correct? a. %(3y3+31y+4x) =0 13' 3 '2 "_J' _ b. \"(3y )+dx(3xy)+dx(4x) _ 0 d1 3 ,9 c. dz(3y +3xy+4x)dx(0) d1 5 2 if _g d. d, (3y )+ dgm) + ux) \"an O a only 0 in only 0 both a and b 0 both c and d Question 2 2 pts If the given equation is 39-3 + 3mg + 43: = 0 and the next step in applying implicit differentiation is to collect all terms involving dy/dx on the left side of the equation and move all other terms to the right side of the equation, which of the following is found on the left side of the equation? 2"? 0. 9y 5 d d b. 9y2+ 31:3\" .1 d a c. 9y3+ 3x+3yd: d. 9y3::+ 3x::+3yE+-1:: Question 3 2 pts If the given equation is 39-3 + 3:83} + 4:13 = 0 and the next step in applying implicit differentiation is to collect all terms involving dy/dx on the left side of the equation and move all other terms to the right side of the equation, which of the following is found on the right side of the equation? *4- 73y 7 4 733? + 4 ans"? . 3x3y4 D Question 12 2 pts Which of the following is the fourth derivative of f(ac) = 325 - 4x3 + 2x2 - 9? a. dx2 = 360x b. day dx2 = 180x2 - 24 C. dx2 = 60x3 - 24x + 4 d. dx2 = 15x4 - 12x- + 4x - 9 O a Ob O c O d D Question 13 2 pts The tenth derivative of f(x ) = 3x5 - 4x3 + 2x2 - 9 is 1. O True O False D Question 14 2 pts The second derivative of 3 In(4x + 1) is 48 (4x+1)2 . O True O False D Question 15 2 pts 32 cos(2x + 5) is the ___ derivative of f(x) = sin(2x + 5).Question 16 5 pts Supposed a circle is expanding in such a way that its radius is growing at a constant rate of 3 inches per minute. How fast is the area of the circle changing at instant that the radius of the circle is 12 inches? 0 56m O 7211 O 8011 o 94;: Question 17 5 pts Supposed a circle is expanding in such a way that its area is growing at a constant rate of 481'! cm2 per second. What is the length of the radius of the circle if the radius is changing at a rate of 6 cm per second? 04 05 05 Q7 Question 18 5 pts A ladder that is 10 meters long is sliding down along a vertical wall. How fast is the ladder's top sliding down the wall when the base is 8 ft from the house and it is moving horizontally at the rate of 3 ft/sec? 0-13 03 Ova 04 Question 19 5 pts Soybeans, pouring down from a chute at a constant rate of 2471' m3/min, form a conical hill. Assuming that the height of the hill is always twice the radius of its base, nd the rate at which the height is increasing when the height is 4 m. Hint: The volume of a cone of radius r and height h is V = 7rr2 h. 03 06 09 012