Can you show step by step for question 5 a and b?

I would like the method used by my teacher below. (BLUE PAPER)

Come up? (0,3) ( 5, 6) d) At what values of x does f have a point of inflection? X = 3, 5, 6 4. Analyze and sketch the graph of f(x) = x3 + 6x2 -1. State e a) the intervals of increase/decrease my"" /jubils b) the local maximum/minimum points c) the intervals where f is concave up/concave down d) the points of inflection 5. Use the guidelines to sketch each of the following: X a ) y = by= x2 - 9 X2 + 4Calculus 12 4.5 Self Assessment (Self Assessment 4) (intel CORE 15 E1) Use the guidelines to sketch f(x) = Guidelines x2 +9' a) Domain XER There is nothing that makes the dencomingfor o b) Intercepts X- int - = X? = 0=*= 10 yint * 2+9 f (o ) = 0 0 4 4 9 * =0 c) Symmetry f ( - * ) = ( - * * ( - *) 4 9 A = f ( x ) even, about the y-axis d) Asymptotes about the yee 10 vertical asymptote because domain is to R Hori asy : lim * 2 2 x 2 y = 1 8 x ( x + 2 ) ? (* + 2 ) 2 e) Intervals of increase or decrease 18 x f (x ) + fly) = ( x3 9) ( 2* ) - [x 2 ) (2* ) X >O Increasing : (0, 00 ) + ( * 2 +9 ) ? Decreasing: (-on,6 ) incre = 27 +18 x - 285 Del ( ( ( ( 249 ) 2 18 18x Y= D 2x 2 flux) exist for demonormalfor weran an make it a - 8 (3x 2 - 4 ) = - 51 5 x - ( X +2 ) 3 ( X - 213 -8 13x - 47 ( X ( x 2 - 4) 3 X 13 [ / x ) = 18 x 2 + 162 - 72 * L ( * 2 + 9 ) 3 s" (x ) = - 54x2 + 162 conc up : ( - 8 (3 ) - 54 (x 2- 3) Cone down : (-00, -13 ) (3) 0 ) ( x 2 + 5)3 ( * 2 4 9 ) 3 f ( x ) = 0 when x 23 = 0 * 2 = 3 f ( 153 ) = 1813 ) ? ficel crist for deummator int point ! " y = 1 103/ 41 -13