Find an equation for the line tangent to the graph of y = tan - 1 x at the point (4,It / 4). What is the tangent line to y = tan - 1 x at the point (4,It / 4)? y (Type an exact answer, using it as needed.)A boat is towed toward a dock by a cable attached to a winch that stands 12 ft above the water level (see figure). Let 6 be the angle of elevation of the winch and let L be the length of the cable as the boat is towed toward the dock. Complete parts (a) to (c) below. d6 a. What is the rate of change of 6 with respect to L, E? d6 - 12L v 0'9 ' 12 dL (L2_144 dL L1/L2-144 d6 _ - 12L d9 _ 12 dL (L2_12 dL LJL212 d6 b. Compute E when L = 50, 20, and 13 ft. d9 When L = 50 ft, E = . (Round to four decimal places as needed.) \fSelect all the boxes and then use the slider to complete the following sentence. If the tangent line to y = f(x) at (X .yo ) is horizontal, then the corresponding line tangent to fat (yoxo) is (Use the interactive figure to find your answer.) Click here to launch the interactive figure. . . . Choose the correct answer below. O parallel to y = x O vertical O horizontal O perpendicular to y = xFind the derivative of the inverse of the given function at the specified point on the graph of the inverse function. f(x) = 5x3 - 9x2- 2, x 2 1.5; (398,5) . . . (f-1) '(398) = (Type an integer or a simplified fraction.)