← Let f(x) = 2√x -x. a. Find all points on the graph of f at which the tangent line is horizontal. 1 b. Find all points on the graph of f at which the tangent line has slope 2 The tangent line is horizontal at the point(s). (Simplify your answer. Type an ordered pair. Use a comma to separate answers as needed.) 1 - The tangent line has slope of 2 (Simplify your answer. Type an ordered pair. Use a comma to separate answers as needed.) at the point(s) ***

+ 3. An amusement park is planning a new roller coaster. Part of it is to have the shape of the cosine function. The high and low points of this part differ by 24 meters and cover a horizontal distance of 40 meters from the high point to the low point. The low point is 6 meters below ground in a tunnel. Let y repre- sent the number of meters the track is above or below ground, and let x repre- sent the number of meters the track is horizontally from the high point. a. Sketch this situation. b. The equation y = 12 cos (4.5x) + 6 models the situation when x and y are in meters and 4.5 is in degrees per meter. Rewrite y = 12 cos (4.5x) + 6 as an equation for which the coefficient of x is in radians per meter. c. What is the length of a vertical support girder at the high point? At a dis- tance of 6 meters horizontally from the high point? At a distance of 20 meters horizontally from the high point? d. Measured horizontally, how far from the high point does the roller coaster enter the…

Graph the given equation by evaluating integer values of x from – 2 to 2 and plotting the resulting points. 3 y = + 2 Answer Keyp Keyboard Shor When you have finished plotting all 5 points, select the button to connect the points and draw the function. Points can be moved by dragging or using the arrow keys. 41 Connect Points Clear -2 -41

Use the graph of f to find the y-intercept, Where applicable, use interval notation.