A meteorologist measures the atmospheric pressure P (in kilograms per square meter) at altitude h (in kilometers). The data are shown below. Use the regression capabilities of the graphing utility to find a linear model for the revised data points obtained by plotting the points . ​ 0 5 10 15 20 ​ ​

A valve on a storage tank is opened for 4 hours to release a chemical in a manufacturing process. The flow rate R (in liters per hour) at time t (in hours) is given by the linear model . Write the linear model in exponential form. ​

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. ​