Please answer all questions and show work for every question. Please provide a step by step explanations, circle the answers, and write neatly as possible. Thank you!

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Show all your work, unsupported answers will receive no credit. Use correct mathematical notation at all times, points will be deducted for incorrect notation. Write your answers to applied problems in complete sentence form with appropriate units. Box your answers. 1. Let f (x) = -6x4+8x3 - 2. a) Find all critical points for f. b) Find the intervals where f is increasing and decreasing. c) Find all local extrema. Indicate the value of each local maximum and local minimum and indicate where each maximum occurs (x-value).2. Let g(x) = x4 - 2x3 - 5x + 3. a) Find the intervals where g is concave up and concave down. b) Find the coordinates of all inflection points. Your answer(s) should be written as points (x, y).3. Use the table of values and the sign charts below to sketch the graph of y = f(x). Assume that the function is continuous on (-co, co). On your graph, you must include the coordinates of all local maxima, local minima, and inflection points. On your graph, indicate whether these points are local maxima, local minima, or inflection points. You may use the following labels: Lmax (local max), Lmin (local min), Pol (point of inflection). X -4 -2 0 3 5 5 A f (x) 0 -2 ND + + +0 - X f" + + + + + + ND - - - - - 0+++++++ X -2