I must sketch the following function (curve) f(x)=(2x-1)^2 (x^2-9) I must show step by step how I got to the answer Derivatives, critical number and so on

2 2
2
( ) (2 1) ( 9)
I) domain of this function is (- , )
II)on factorizing
( ) (2 1) ( 3)( 3)
1
( ) 0 at 3, ,3
2
1
also, ( ) has repeated root at
2
graph will cut x axis at x=-3,3 and
f x x x
f x x x x
Roots
f x x
f x x
hence
  
 
   

  

2
1
touch x axis at x=
2
III) (0) (0 1) (0 9) 9
graph will cut y axis at (0,-9)
(IV) sign Diagram for f (x)-
f
hence
    
Sign will not change about x=1/2 as it is 2 times...