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

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

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. ​