Hello, I need help with calc, take your time, thank you.

(1 point) The graph of x) is shown below. Choose the best sketch of f'(a':). 6 10 2 6 10 A B C 2 6 10 6 10 2 6 10 D E F(Note: the vertical axes of these graphs may have been scaled to to t these functions. Click on a graph to enlarge it.) Which of the following statements are true? Select all that apply. C] A. If v'(t) is zero, then U(t) must be zero. C] B. The function t)' represents the acceleration of the car. C] C. When v'(t) is negative, the car is moving backwards. C] D. There are times when 'v'(t) is zero and 0(t) is not zero. [3 E. The function t)' represents the position of the car. C] F. When U(t) is positive, v'(t) must also be positive. [3 (3. When v'(t) is negative, the car is slowing down. [3 H. None of the above statements are true. (1 point) The limit lim w h represents 1\" (a) for some function f and some number 0.. Find x) and a. hH) it?) = a: (1 point) Let 3222: 3:54 f($):{2a: a:>4 (a) Is f continuous at a: = 4 ? v (b) Is f differentiable at :1: = 4 ? v (c) If f is differentiable at a: = 4 enter the value of f'[4). If f is NOT differentiable at a: = 4 enter the value of f(4) instead. f'(4) 0r f(4) = (1 point) At what point does the normal to y = 5x - 4 + 3x2 at (1, 4) intersect the parabola a second time? Answer: Note: You should enter a cartesian coordinate. The normal line is perpendicular to the tangent line. If two lines are perpendicular their slopes are negative reciprocals -- i.e. if the slope of the first line is m then the slope of the second line is -1/mChoose the correct letter. ? | If you are having a hard time seeing the picture clearly, click on the picture. It will expand to a larger picture on its own page so that you can inspect it more clearly. A. B. C. D.(1 point) The tangent line to y : f(23) at (3, 8) passes through the point (10, 2). Compute the following. a.) M) = b.1f'(3) = (1 point) The graphs of the function F (left, in blue) and G (right, in red) are below. Let P(:I:) : F($)G($) and Q(:I:) : F(a:)/G(;c). Answer the following questions. _____________________________________________ ---------------------------------------------- ______________________________________________ 2. c211) = 3. P'(6) : 4- (2'05) (1 point) Consider the slope of the given curve at each of the five points shown. List these five points in decreasing order of the slopes. VA A E B D C 0(1 point) For the following function whose graph is shown, choose the graph below that corresponds to its derivative. (click on image to enlarge) y = at) (click on images to enlarge) (a) j (b) (C) (d) Select correct option from below. ? v Let m) be the function whose graph is shown below. 1. Determine f'(a.) for a. = 1, 2, 4, 7. HI) = \\ \\ H2) = \\ \\ H4) = \\ \\ H7) = \\ \\ (1 point) Suppose that the oost of manufacturing 2: pairs of shoes is C = f(a:) dollars. (a) What are the units of f '(m)? (Write each word in its entirety, in lower case). Units: I (b) If you've already manufactured 290 pairs, estimate the cost of manufacturing an additional pair if f '(290) = 1200. Cost: The position (in thousands offeet} of a car driving along a straight road at time t in minutes is given by the function y = 3(t) that is pictured below. Let v(t) denote the velocity of the car (in thousands of feet per minute) at time t (in minutes). Which graph A-F is the best representative of the derivative function if (t)? ? v