MATH1680.120Sample Test 2Last Name:First Name:TI-30XA calculator may be used.Books, notes, or otherelectronic devices are not permitted. Do not use your ownpaper. To receive credit you must show necessary work onthe test pages. Do not leave negative or fractional powersin your final answers.Problem 1.Use the given graph offto fill in the blanks.The functionfis increasing on the interval(s)and decreasing on the interval(s). The functionfis concaveon (-1,-1), concaveon(-1,3), and concaveon (3,1). The graph has vertical asymptoteand horizontal asymptote. The functionfas a relativeatx= 2.Problem 2.Give the equations of all vertical and horizontal lines which are asymptotes to thegraph off(x) =(2-x)(6x+ 3)2x2+ 6x-20.
Problem 3.Find the absolute minimum and absolute maximum off(x) =x4-2x3on [1,2].Problem 4.Find the intervals of concavity and inflection points for the functionf(x) =x4-x2.Problem 5.Graph a functionfwhich has the following properties.
Problem 6.Letf(x) = 2-15x+ 9x2-x3.(a) Find the maximal open intervals on whichfis increasing or decreasing, respectively. (You maydepict the intervals schematically, on the line below.)(b) Find the maximal open intervals on whichfis concave up or concave down, respectively. (Youmay depict the intervals schematically, on the line below.)(c) Identify and classify all relative extrema and inflection points off, and compute the values offat those points.(d) Determine the limits off(x) asx! -1and asx! 1.
(e) Sketch the graph off. Begin by plotting the points from part (c).Problem 7.The figure below shows the graph of the equation 2x2+ 8xy=y3, which implicitlydefinesyas a function ofx.Determine the slopedydxalong the curve, wherever it is defined.