PrOblem #1: The graph of f is given to the right. Which of the below graphs is a graph of its derivative f "? (A) (C) (E) (G) (H) Problem #1: Select V l Just Save I I Submit Problem #1 for Grading Problem #1 Attempt #1 Attempt #2 Attempt #3 Your Answer: Your Mark: PrOblem #2: The graph of g is given to the right. Which of the below graphs is a graph of its derivative g"? 1' Problem #2: Select V I Just Save I I Submit Problem #2 for Grading I Problem #2 Attempt #1 Attempt #2 Attempt #3 Your Answer: Your Mark: Problem # 3: Find the values of a and b so that the parabola y = ax2 + bx has a tangent line at (1, 2) with equationy = 7x 9. Problem #3: |:| enter your answer in the form a,b [ Just Save l l Submit Problem #3 for Grading Problem #3 Attempt #1 Attempt #2 Attempt #3 Your Answer: Your Mark: Problem #4: Let 14(96): 2g(x) . 6+f(X) Suppose that f(2) = *2,f'(2) = 4, g(2) = *3, and g'(2) = 2. Find h'(2). - |:| Enter your answer symbo'ical'y' Problem #4' as in these examples [ Just Save l l Submit Problem #4 for Grading Problem #4 Attempt #1 Attempt #2 Attempt #3 Your Answer: Your Mark: Problem #5: (a) Suppose that the tangent line to the curve y = f(x) at the point (-9, -65) has equation y = -2 + 7x. If Newton's method is used to locate a root of the equation f(x) =0 and the initial approximation is x1 = -9, find the second approximation x2. (b) Suppose that Newton's method is used to locate a root of the equation f(x) = 0 with initial approximation x1 = 4. If the second approximation is found to be x2 = -9, and the tangent line to f(x) at x = 4 passes through the point (16, 4), find f (4). (c) Use Newton's method with initial approximation x1 = 2 to find x2, the second approximation to the root of the equation x' = 3x + 3. Problem #5(a): Enter your answer symbolically, as in these examples Problem #5(b) : Enter your answer symbolically, as in these examples Problem #5(c): Enter your answer symbolically, as in these examples Just Save Submit Problem #5 for Grading Problem #5 Attempt #1 Attempt #2 Attempt # 3 Your Answer: 5(a) 5(a) 5(a) 5(b) 5 (b) 5 (b) 5 (c ) 5 (c ) 5 (c ) Your Mark: 5(a) 5(a) 5(a) 5(b) 5 (b) 5 (b ) 5 (c ) 5 (c ) 5 (c )Problem #6: Let F(x) =f(xf(x2)). Suppose that f(4) = 5, f'(4) = 1, and f'(10) = 2. Find F'(2). Problem #6: Just Save Submit Problem #6 for Grading Problem #6 Attempt #1 Attempt #2 Attempt #3 Your Answer: Your Mark:Problem #7: Let f and g be the functions whose graphs are shown below. f(x ) 4 -3 2 3 4 5 -1 X g(x) (a) Let u(x) = f(x)g(x). Find u'(-3). (b) Let v(x) =f(f(x)) . Find v'(4). Problem #7(a): Enter your answer symbolically, as in these examples Problem #7(b): Enter your answer symbolically, as in these examples Just Save Submit Problem #7 for Grading Problem #7 Attempt # 1 Attempt # 2 Attempt # 3 Your Answer: | 7(a) 7 (a ) 7 (a) 7(b) 7 (b) 7 (b ) Your Mark: |7(a) 7(a) 7(a) 7 (b ) 7 (b ) 7 (b )PrOblem # 8: Find an equation of the tangent line to the curve y : tan2(x) at the point (7t/4, 1). Put your answer in the form y = mx + b, and then enter the values of m and b in the answer box below (separated with a comma). - as In these examples enter your answer in the form m,b Just Save Submit Problem #8 for Grading Problem #8 Attempt #1 Attempt #2 Attempt #3 Your Answer: Your Mark: Problem #9: Let f(x) = e . Find a simplified expression for f"(x). (A) -47e 8x - 45 6.x - 45 7x + 48 x12 (B) -45e (C) 45e (D) 47e 6.x3 + 45 7 12 (E) -47e 8x - 45 (F) -45e 6.x5 - 45 (G) 47e 7x+ 48 712 (H) 45e 6.x+ 45 ro Problem #9: Select v Just Save Submit Problem #9 for Grading Problem #9 Attempt # 1 Attempt #2 Attempt #3 Your Answer: Your Mark