A rectangular page is to contain 36 square inches of print. The margins on each side are 1 inch. Find the dimensions of the page such that the least amount of paper is used. ​

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

A solid is formed by adjoining two hemispheres to the ends of a right circular cylinder. The total volume of the solid is 23 cubic centimeters. Find the radius, r, of the cylinder that produces the minimum surface area. Round your answer to two decimal places. ​

A ball bearing is placed on an inclined plane and begins to roll. The angle of elevation of the plane is radians. The distance (in meters) the ball bearing rolls in t seconds is . Determine the value of after one second. Round numerical values in your answer to one decimal place. ​

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  . ​