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. ​

The sum of the perimeters of an equilateral triangle and a square is 8. Find the dimensions of the triangle and the square that produce a minimum total area. ​

Find the  x- values (if any) at which is not continuous. ​

Find the constant a and b such that the function ​ ​ is continuous on the entire real line. ​

Let and . Find the limit. ​ ​