Exam 4: Applications of Differentiation

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

Find the point on the graph of the function that is closest to the point . ​

Find all points of inflection on the graph of the function . ​

Find the limit. ​ ​

Find the relative maxima of on the interval by applying the First Derivative Test. Round numerical values in your answer to three decimal places. ​

A sector with central angle is cut from a circle of radius 11 inches, and the edges of the sector are brought together to form a cone. Find the magnitude of such that the volume of the cone is a maximum. ​

The total stopping distance T of a vehicle is where T is in feet and x is the speed in miles per hour. Use differentials to approximate the percent change in total stopping distance as speed changes from to miles per hour. Round your answer to one decimal place. ​

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

Find all critical numbers of the function , . ​

Use a computer algebra system to graph the function and determine all absolute extrema on the interval . ​

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

Find the equation of the tangent line T to the graph of at the given point . ​

On a given day, the flow rate F (cars per hour) on a congested roadway is given by , where v is the speed of the traffic in miles per hour. What speed will maximize the flow rate on the road? Round your answer to the nearest mile per hour. ​

Sketch a graph of the function over the interval . ​