The graph of a function f is shown below. Sketch the graph of the derivative . ​ ​

Find the value of the derivative (if it exists) of the function  at the extremum point  . ​

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. ​ Use a graphing utility to confirm your results. ​

Determine the x-coordinate(s) of any relative extrema and inflection points of the function . ​

Find all points of inflection, if any exist, of the graph of the function . Round your answers to two decimal places. ​

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. ​

A container holds 6 liters of a 25% brine solution. A model for the concentration C of the mixture after adding x liters of an0.88 % brine solution to the container and then draining x liters of the well-mixed solution is given as . Find . Round your answer to two decimal places. ​

The radius of a spherical balloon is measured to be 8 inches, with a possible error of 0.08 inch. Use differentials to approximate the maximum possible error in calculating the volume of the sphere. Round your answer to two decimal places. ​

Use a graphing utility to graph the function and locate the absolute extrema of the function on the interval . ​

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. ​