I need to figure out what the graph of f(x)= 1 / (2-3x)^3 near x=2/3 would look like.

1 answer

1. f'=-3(-3)/(2-3x)^4
   f"=-36/(2-3x)^5
   
   now look at f', and f" at each side of 2/3, say at .5, and at 1.0
   
   I will do the 1.0 side...
   f=1/(2-3)^3=1
   f'=9/(2-3)^4= positive 9, high slope
   f"=-36/(2-3)^5=36 positive, curving up
   
   now the .5 side.
   f=1/(2-1.5)^3=8
   f'=9/(2-1.5)^4=9*64 positive, going upwards
   f"=-36/(.5)^5=-1152 negative curving down,slope is reducing.
   
   Now graph it on your calculator and take a look

   Answer ID
   524413

   Created
   April 2, 2011 11:12pm UTC

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   0

   URL
   https://questions.llc/answers/524413