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(2 points) Consider the function f(x) = = 3+ ex Then S'(x) = The following questions ask for endpoints of intervals of increase or decrease for the function f(x). Write INF for co, MINF for -co, and NA (ie. not applicable) if there are no intervals of that type. The interval of increase for f(x) is from to The interval of decrease for (x) is from to (x) has a local minimum at (Put NA if none.) (x) has a local maximum at (Put NA if none.) Then f"(x) = The following questions ask for endpoints of intervals of upward and downward concavity for the function f(x). Write INF for co, MINE for -co, and put NA if there are no intervals of that type. The interval of upward concavity for f(x) is from The interval of downward concavity for /(x) is from (x) has an inflection value, x = . (Put NA if none.) (1 point) Below is the graph of the derivative /'(x) of a function defined on the interval (0,8). You can click on the graph to see a larger version in a separate window. Refer to the graph to answer each of the following questions. For parts (A) and (B), use interval notation to report your answer. (if needed, you use U for the union symbol) (A) For what values of x in (0,8) is /(x) increasing? (If the function is not increasing anywhere, enter None .) Answer. (B) For what values of x in (0,8) is /(x) concave down? (if the function is not concave down anywhere, enter None .) Answer. (C) Find all values of x in (0,8) is where f(x) has a local minimum, and list them (separated by commas) in the box below. (If there are no local minima, enter None .) Local Minima: (D) Find all values of x in (0,8) is where f(x) has an inflection point, and list them (separated by commas) in the box below. (If there are no inflection points, enter None .) Inflection Points: (1 point) A function is said to have a horizontal asymptote if either the limit at infinity exists or the limit at negative infinity exists. Show that each of the following functions has a horizontal asymptote by calculating the given limit. lim -10x x-+00 6 + 2x 12x - 7 lim 1-+-00 x3 + 4x - 11 lim x2 - 7x - 4 x-+0 15 - 15x2 lim Vx2 + 10x X-+00 8 - 7x Vx2 + 10x lim x-+-00 8-7x