...................

Let f(:c) : 71:4 7 3::3 + 71' 7 6. Find the open intervals on which 1' is concave up (down). Then determine the accoordinates of all inection points of f. 1. f is concave up on the intervals 2. f is concave down on the intervals 3. The inection points occur at :1: = Notes: In the first two, your answer should either be a single interval, such as (0,1), a comma separated list of intervals, such as (-inf, 2), (3,4), or the word "none". In the last one, your answer should be a comma separated list of :r values or the word "none". Below is the graph of the derivative f'(:n) of a function defined on the interval (0,8). You can click on the graph to see a larger version in a separate window. e (A) Forwhat values ofa: in (0,8) is f(z) increasing? Answer: C] Note: use interval notation to report your answer. Click on the link for details, but you can enter a single interval, a union of intervals, and if the function is never increasing, you can enter the empty set as { }. (B) Find all values of 1: in (0,8) is where f($) has a local minimum, and list them (separated by commas) in the box below. If there are no local minima, enter None. Local Minima: C] Below is the graph of the derivative f (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 part (A), use interval notation to report your answer. (If needed, you use U for the union symbol.) (A) For what values of a in (0,8) is f(a) concave down? (If the function is not concave down anywhere, enter "{}" without the quotation marks.) Answer: (B) Find all values of a in (0,8) is where f( ) has an inflection point, and list them (separated by commas) in the box below. (If there are no inflection points, enter -1000.) Inflection Points