NOTE: When using interval notation in WeBWorK, remember that: You use 'INF' for 00 and 'tNF' for 00. And use 'U' tor the union symbol. Enter DNE it an answer does not exist. z} = :3 + 1232 16 a} Give the domain of f (in interval notation) E| b) Find the critical numbers of f. - - {Separate multiple answers by commas.) c) Determine the intervals on which f is increasing and decreasing. f is increasing on: I I f is decreasing on: d) Use the First Derivative Test to determine whether each critical point is a relative maximum, minimum, or neither. Relative maxima occur at z = (Separate multiple answers by commas.) Relative minima occur at z = (Separate multiple answers by commas.) f(x) = -2x3+ 18x2 + 42x - 8 is increasing on the interval ( It is decreasing on the interval ( -00, ) and the interval ( , 00 ) . The function has a local maximum atDetermine the intervals on which f is increasing or decreasing, assuming the figure below is the graph of the derivative of f. On Interval 1: f is On Interval 2: f is ? On Interval 3: f is ?f(x) = 6(x -8)2/3 +6. (A) Find all critical values and list them below. Note: If there are no critical values, enter 'NONE' (B) Use interval notation to indicate where f () is increasing. Note: Use 'INF' for co, '-INF' for -oo, and use 'U' for the union symbol. Increasing: (C) Use interval notation to indicate where f () is decreasing. Decreasing: (D) List the a values of all local maxima of f. If there are no local maxima, enter 'NONE'. c values of local maximums = (E) List the c values of all local minima of f. If there are no local minima, enter 'NONE'. c values of local minimums =