Question

= 2, and you We consider some function () whose domain of g is all real numbers except are given and g" as follows: ' ) = e't-3) (1-2)2 (r - 2) "(t)er? - 6r + 10) a) Find all points where ) = 0 or g'(c) does not exist. Give a sign diagram for g'(x). Indicate where g is increasing or decreasing. Find all local minima and maxima of g(x). b) Find all points where g" (x) = 0 or g" (x) does not exist. Give a sign diagram for g" ). Indicate where g is concave up or concave down. Find all inflection points of g(x). c) You are given the following information about g: lim g(x) = 0 lim g(x) = + lim g(x) = - lim g(x) = + Make a sketch of g(x).

Please help and show steps. Thank you.

Answer 1

Date: / Page no Given, q!(X) = ė (x-3) Co=23 "(x) = x (x² - 6x +10) a (1-2) Partla) Either ex = 0 or (2-3) = 0 u=3 x-001 and Are the points where g'(x)=0,

Date:_, , Page no: At does (4-2)=0 not exists. the le = 2, 2 point where olla) does not exists. These are I called poles. -{9"(x) = o } I en (x² - 6x +10) - 24-243 » Either e"=o or (x²- 62 +10)=0 [x- & x= 6 I 136-40 These are the points whore. 9000 =0.

Date: / / Page no: - 2 At {x-2) = 0 x=2, 2, 2 These are the points where d'a) does not exists. Finding 9" (x) at [x=31 If gu() 30 » concave up. If 9! (2) 20 7 Concave down. q"(3) = ēs (9-18+10) ANSWER Concave Up

Date: 11 _Page no:_ • Point of Inflection of g(x) → These point can occur where the second derivative is zero. And we know that, At x= 3+21 / " (2 At I = 3121 becomes Zero.