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Determine whether the Mean Value Theorem can be applied to the function on the closed interval . If the Mean Value Theorem can be applied, find all numbers c in the open interval such that . ​

The graph of f is shown in the figure. Sketch a graph of the derivative of f. ​ ​

Use the graph of the function given below to estimate the open intervals on which the function is increasing or decreasing. ​ ​

Use differentials to approximate the value of . Round your answer to four decimal places. ​

The range R of a projectile is  where ν0 is the initial velocity in feet per second and θ is the angle of elevation. If ν0 = 2200 feet per second and θ is changed from 12° to 13° use differentials to approximate the change in the range. Round your answer to the nearest integer. ​

Find the point of inflection of the graph of the function on the interval . ​

The height of an object t seconds after it is dropped from a height of 500 meters is . Find the time during the first 4 seconds of fall at which the instantaneous velocity equals the average velocity. ​

Locate any relative extrema and inflection points of the function . Use a graphing utility to confirm your results. ​

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 ​ ​

Find the open interval(s) on which is increasing or decreasing. ​