Exam 1: Functions, graphs, and Limits

​Find the derivative of the following function using the limiting process. ​ ​ ​

​Sketch the graph of the function using any extrema,intercepts,symmetry,and asymptotes. ​

​Find the x-values of all relative maxima of the given function. ​ ​ ​

​Find the limit. ​ ​ ​

​Compare dy and Δy for at ​x​ = 1 with dx = -0.01.Give your answers to four decimal places. ​

​Find the derivative of the function. ​ ​ ​

A wooden beam has a rectangular cross section of height h and width w (see figure).The strength S of the beam is directly proportional to the width and the square of the height.What are the dimensions of the strongest beam that can be cut from a round log of diameter d = 26 inches? Round your answers to two decimal places.[Hint: where k > 0 is the proportionality constant.] ​