Problem #9: Let f(x) = e . Find a simplified expression for f"(x). (A) -43e 12x9 - 45 7-20 (B) 45e 11x + 47 ( C ) - 45e 10x9 - 45 3-22 ) (D) 45e 10x + 45 3-22 (E) -45e 10x - 42) (F) 43e 10x + 42) (G) 43e 3-20 1 1x +47) (H) -49e 12x9 - 45 x-22 3-20 x-22Problem # 2: The graph of g is given to the right. Wleh of the below graphs is; a graph of its derivative 3*"? (A) J (C) (E) (F) (G) (H) I Problem # 8: Find an equation of the tangent line to the curve y = tangbc) at the point (IE-".3. 3]. Put your answer in the form y = mx I). and then enter the values of m and I) in the answer box below (separated with a comma). Problem #7: Let fand g be the functions whose graphs are shown below. g(x) 2 4 2 A X -2 F(x) 4 (a) Let u(x) =f(x)g(x). Find u'(3). (b) Let v(x) = g(g(x)) . Find v'(-2).Problem #5: (a) Suppose that the tangent line to the curve y =f(x) at the point (1, -16) has equation y = -7 - 9x. If Newton's method is used to locate a root of the equation f(x) =0 and the initial approximation is x, = 1, 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 = 5. If the second approximation is found to be x2 = -2, and the tangent line to f(x) at x = 5 passes through the point (18, 9), find f(5). (c) Use Newton's method with initial approximation x1 = 7 to find x2, the second approximation to the root of the equation x' = 9x - 9.Problem #3: Find the values of a and b so that the parabola y = ax+ bx has a tangent line at (1, -7) with equation y = -9x + 2. Problem #3: enter your answer in the form a,bProblem #6: Let F(x) =f(xf(x2)). Suppose that f(4) = 3, f'(4) = 3, and f'(6) = 5. Find F'(2). Problem #6:Problem #4: Let h(x) = 6g(x) 9+f(x) Suppose that f(2) = -3. f'(2) = 1, g(2) = -4, and g'(2) = 4. Find h'(2).Problem #1: The graph of f is given to the right. Which of the below graphs is a graph of its derivative f"? (A) (B) (C) (D) (E) (F) (G) (H)