Please answer the following questions, show all the steps.

Assignment 6: Problem 3 (1 point) Let at) = 10 + 122:: 333. Find (a) the intervals on which f is increasing, (b) the intervals on which f is decreasing, (c) the open intervals on which f is concave up, (d) the open intervals on which f is concave down, and (e) the $ coordinates of all inflection points. a) f is increasing on the interval(s) b) f is decreasing on the interval(s) ( ( (c) f is concave up on the open interval(s)C] (d) f is concave down on the open interval(s)D ( e) the m coordinate(s) of the points of inflection are C] Notes: In the first four boxes, 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 box, your answer should be a comma separated list of 33 values or the word "none". Assignment 6: Problem 6 [1 point) Let at) = :r:4 81:3 + 3:1: + 6. Find the open intervals on which f is concave up (down). Then determine the ac 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". Assignment 6: Problem 7 (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. . 8m wioo 9 + 2m _ 3:2 12:13 15 D 11m = :si-oo 13 13m2 . 1:2 + 13m [3 11m = $>00 10 13$ Note: You can earn partial credit on this probiem. Assignment 6: Problem 5 (1 point) 1 Let at) _ 73:2 + 4 concave up (down). Then determine the mcoordinates of all inflection points of f. (inflection points are where I\" = u). . Find the open intervals on which f is 1. f is concave up on the intervals 2. f is concave down on the intervals 3. The inflection points occur at as = 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 :1: values or the word "none". Assignment 6: Problem 4 (1 point) On what intervals is the function f(x ) = x3 - 3x2 both decreasing and concave up? interval(s) = (Give your answer as an interval or a list of intervals, e.g., (- infinity,8] or (1,5), (7, 10) .)