Find the inflection points of x) 2 81:4 + 110333 42932 l 14. (Give your answers as a comma separated list, e.g., 3,-2.) inflection points =l l 9:\":1} The graphs above are approximate graphs of f and f' for 1%) = 27%? 9)- 50 f is decreasing {and f' is negative) on the interval [0, a) for a, 2' '. (Give the largest a that works.) Let f(ac) = a2 - 5x - 6. Find the open intervals on which f is concave up (down). Then determine the x-coordinates of all inflection points of f. 1. f is concave up on the intervals 2. f is concave down on the intervals 3. The inflection points occur at ac 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 a values or the word "none".f(ac) = 4ac5 - 4x4. Instructions: If you are asked to find a- or y-values, enter either a number, a list of numbers separated by commas, or None if there aren't any solutions. Us interval notation if you are asked to find an interval or union of intervals, and enter { } if the interval is empty. (a) Find the critical numbers of f, where it is increasing and decreasing, and its local extrema. Critical numbers x = Increasing on the interval Decreasing on the interval Local maxima x = Local minima x = (b) Find where f is concave up, concave down, and has inflection points. Concave up on the interval Concave down on the interval Inflection points a =Suppose that f(ac) = 23 - 2202 + 14. (A) List the a values of all local maxima of f. If there are no local maxima, enter 'NONE'. values of local maximums = (B) List the a values of all local minima of f. If there are no local minima, enter 'NONE'. a values of local minimums = (C) List the a values of all the inflection points of f. If there are no inflection points, enter 'NONE'. * values of inflection points =Below is the graph of the derivative f'(m) of a function defined on the interval (08). 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 :L' in (0,8) is f(.7:) increasing? (If the function is not increasing anywhere, enter None .) Answer: l l (B) For what values of a: in (0,8) is f(w) concave down? (If the function is not concave down anywhere, enter None.) Answer: l l (C) Find all values of m in (0,8) is where f(:c) has a local minimum, and list them (separated by commas) in the box below. (If there are no local minima, enter None -) Local Minimazl l (D) Find all values of :c in (0,8) is where 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: '7' Let f be the function with domain [1, 3] defined by f(:c )= im2 + 311:. The function f has a global maximum at a: :l: l The function f has a global minimum at a: :l :l. Let f(x) = 8x3 - 1. Find the open intervals on which f is increasing (decreasing). Then determine the x-coordinates of all relative maxima (minima). 1. f is increasing on the intervals 2. f is decreasing on the intervals 3. The relative maxima of f occur at x = 4. The relative minima of f occur at x =Let f(ac) = 23 - 2ac2 + 8ac + 2. Find the open intervals on which f is concave up (down). Then determine the x-coordinates of all inflection points of f. 1. f is concave up on the intervals 2. f is concave down on the intervals 3. The inflection points occur at a = 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 a values or the word "none"