Please answer the following questions about the function f(2) = 425 - 4x4. Instructions: If you are asked to find x- or y-values, enter either a number, a list of numbers separated by commas, or None if there aren't any solutions. Use 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 * = 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 * =Find the inflection points of f(x) = 8x* + 11023 42x2 + 14. (Give your answers as a comma separated list, e.g., 3,-2.)The graphs above are approximate graphs of f and f' for f(x) = ='(x -9). So f is decreasing (and f is negative) on the interval (0, a) for a (Give the largest a that works.)Let f() = x2 -5x - 6. Find the open intervals on which f is concave up (down). Then determine the c-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 c 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 @ values or the word "none".Suppose that f(x) = 2 - 2x2 +14. (A) List the * values of all local maxima of f. If there are no local maxima, enter 'NONE'. c values of local maximums = (B) List the x values of all local minima of f. If there are no local minima, enter 'NONE'. c values of local minimums = (C) List the * values of all the inflection points of f. If there are no inflection points, enter 'NONE'. c values of inflection points =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 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 a in (0,8) is f() increasing? (If the function is not increasing anywhere, enter None .) Answer: (B) For what values of a in (0,8) is f() concave down? (If the function is not concave down anywhere, enter None .) Answer: (C) Find all values of a in (0,8) is where f(2) 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 () has an inflection point, and list them (separated by commas) in the box below. (If there are no inflection points, enter None .) Inflection Points:Let f be the function with domain [1, 3], defined by z) = 7:712 + 32:. The function f has a global maximum at x =D. The function f has a global minimum at m =U. Let f() = 8x-1. Find the open intervals on which f is increasing (decreasing). Then determine the -coordinates of all relative maxima (minima). f is increasing on the intervals 2. f is decreasing on the intervals 3. The relative maxima of f occur at c 4. The relative minima of f occur atLet f() = 8x3 - 1. Find the open intervals on which f is increasing (decreasing). Then determine the c-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 c = 4. The relative minima of f occur at c =Let f(x) = 23 - 2x2 + 8x + 2. Find the open intervals on which f is concave up (down). Then determine the c-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