Compare dy and for at  with . Give your answers to four decimal places. ​

Find the open interval(s) on which the function is increasing in the interval . Round numerical values in your answer to three decimal places. ​

Sketch a graph of the function over the interval . ​

The graph of f is shown. Graph f, f’ and f” on the same set of coordinate axes. ​ ​

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

The resistance R of a certain type of resistor is where R is measured in ohms and the temperature T is measured in degrees Celsius. Use a computer algebra system to find the critical number of the function. Round numerical values in your answer to the nearest whole number. ​

Analyze and sketch a graph of the function . ​

Locate the absolute extrema of the function on the closed interval . Round your answers to four decimal places. ​

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