Answer key is attached, I just need help with showing the work. Please show work with justification, box the final answer, and write neatly. Thank you for your support

AP Calculus Quiz #4 Answer Key & Rubrics Multiple Choice Date 1. D 2. A 3. C B Alatsple Chelice 4. E C 5. C A 6. D 7. A Free Response Part A -3 points total 1 Correctly finds f'(x) = - V2x+ 1 -f' (4 ) = - 2(4 ) + 1 3 - The slope of the tangent line 1 Correctly finds f(4) = 2(4) +1 =3- The point of tangency 1 Equation of the tangent line: y -3 = =(x -4) Free Response Part B -3 points total 1 Correctly finds g'(x) = -sinx- g'(#)=-sin =-1- The slope of the tangent line which Therefore the slope of the normal line would be 2. 3x 1 Correctly finds g( )= cos 1 = 13 - The point of tangency 1 Equation of the normal line: y-2 graph of (() when ? Free Response Part C-3 points total 1 Correctly differentiates to find h'(x) = (-sin x)2x +1 +(cosx) ;(2x+1) 2(2) 1 Correctly evaluates h (31 )= 37 + 1 1 Since hi(32 )> 0, then the graph of h(x) is increasing at x = 31 Daily Lessons and Assessments for AP* Calculus AB, A Complete Course Page 22 Mark Sparks 2012/' ' CALCULUS QUIZ#4 Name Date -- Your Score out of 18 Calculator NOT Permitted tan3(x + h) - tan 3x 1. Find 11m [1)0 h A. sec 3x tan 3x B. sec2 3x C. tan 3x D. 3sec2 3x B. Does not exist 2. If f(x) = 2xsin x, then what is the slope of the tangent line to the graph of x) whenx = g ? W .6 mat NI"I'QN / Daily Lessons and Assessments for AP* Calculus AB, A Complete Course Page 2 Mark Sparks 2012 When x = -1, then the graph of f (x) = -2xVx+2 ... A. is undefined. B. is increasing. C. is decreasing. D. has a vertical tangent. E. has a horizontal tangent. D. SO- 4. What is the slope of the normal line to the graph of the function g(x) = Vx2 -2x when x = 4? A. V8 B. V8 "Weleads table offerings for s(s) and g (xyare given below. If he) - V(). a(x). C. 3V8 pool for the tingcat to the graph of Mir) when x 3? D. 3 V8 E. -2 5. If f (x) = 3x +x -, then f'(x) is S 3x-x 4 A. 1 B. 6x + 1 6x-1 -6 C. (3x- 1)2 - 2x2 D. (x 2 - x) 2 36x3 -2x E. (x2 -x) Daily Lesso nd Assessments for AP* Calculus AB, A Complete Course Page 22If f ( 0 ) = 210 + 3cos0, what is f' ( @ ) ? CA. f'(0) =1+310 cose I and of) - cos . to answer the following questions B. f'(0) = 1 -3sino agent line to the graph of /x) whon x = 4. VO C. f'(0) = 2+310 sino Vo D. f'(0) = 1-310 sino VO E. f'(0) = 1+310 sine VO 7. The graph of f(x) and a table of values for g(x) and g'(x) are given below. If h(x) = Vf(x) . g(x), what is the slope of the line tangent to the graph of h(x) when x =-3? X g(x) g' (x) -3 4 -2 0 -1 -3 3 2 4 2. Graph of f(x) 5 4 A. V8 B. 13 216 C. V8 2 D. 1 218 E. V6b. Find the equation of the normal line to the graph of g(x) when x = % Daily Lessons and Assessments for AP* Mark Sparks 2012 V g c. Suppose that h(x) = g(x) . f(x). Is h(x) increasing or decreasing at x = 3x ? Show your work and give a reason for your answer. Multiple Chaire x (97) S. 6. 7. 1. Find fim Be 2(x )) 4502x A 2sec 2x tan 2x B. sec 2x C. -2800 28 D. soc Ox tan 2x E. Does not exist 2 If f () a Jesusy, then what is the slope of the fanged line B. C. 0Name Date Multiple Choice Your Score out of 18 Calculator NOT Permitted MULTIPLE CHOICE 1. Find \"In sec2(x+h) sec2x . h->0 h A. 25cc 2x tan 2x B. sec 2x C. Zsec2 2): D. sec 2x tan 2x E. Does not exist 2. If f(x) = 2x003 x , then what is the slope of the tangent line to the graph of f(x) When x = l? 2 A. TE B. -n C. 0 D. 2 1 E. 5 Daily Lessons and Assessments for AP" Calculus AB, A Mark Sparks 2012 x 4x A. is undened. B. is increasing. C. is decreasing. D. has a vertical tangent. E. has a horizontal tangent. H . f 2 _ = 4? What 1s the slope of the normal line to the graph of the mctlon g(x) = x 2 when x 36 321: E. L Daily Lessons and Assessments for AP" Calculus AB, A Co ..;; Mark Sparks 2012 6. If f(0) =210 +3sin0, what is f'(@)? A. f'(0) _ 1+ 310 sine 12 4 1 and guy s coax in ma warand following questions. a. Flad B. f'(0) = 1 -3cos0 at live to the gough of 10 when s -4. C. f'(0) = 2+310 coso D. f.(0) = 1-310 cose E. f(0) = 1+310 cose 7. The graph of f(x) and a table of values for g(x) and g'(x) are given below. If h(x) = Vf(x) . g(x), what is the slope of the line tangent to the graph of h(x) when x = 3? g(x g'(x) 4 find the -3 -2 of you wive 0 -1 -3 3 2 -4 5 4 Graph of f(x) A. B. 2V8 C. V8 2 D. 13 216 E. V6 Daily Lessons and Assessments for AP* Calculus AB, A Complete Course Page 229 Mark Sparks 2012b. Find the equation of the normal line to the graph of g(x) when x = 25 Daily Lessons and Assessments for AP* Calculus AB, A C a Mark Sparks 2012 c. Suppose that h(x) = g(x) . f(x). Is h(x) increasing or decreasing at x = 3x ? Show your work and give a reason for your