For the function : ​ (a) Find the critical numbers of f (if any); (b) Find the open intervals where the function is increasing or decreasing; and (c) Apply the First Derivative Test to identify all relative extrema. ​ Then use a graphing utility to confirm your results. ​

Identify the open intervals where the function is increasing or decreasing. ​

A ball bearing is placed on an inclined plane and begins to roll. The angle of elevation of the plane is radians. The distance (in meters) the ball bearing rolls in t seconds is . . Determine the speed of the ball bearing after t seconds. ​

Find all points of inflection of the graph of the function on the interval . Round your answer to three decimal places wherever applicable. ​

Analyze the graph of the function . Determine any intercepts, relative extrema, points of inflection and asymptotes. Also determine where the graph is increasing or decreasing and concave up or concave down. Then identify the graph from the choices below. ​

Find the points of inflection and discuss the concavity of the function on the interval . ​

Compare dy and for at  with . Give your answers to four decimal places. ​

Find the open interval(s) on which the function is increasing in the interval . Round numerical values in your answer to three decimal places. ​

Sketch a graph of the function over the interval . ​

The graph of f is shown. Graph f, f’ and f” on the same set of coordinate axes. ​ ​