October 23rd, 2013, 10:10 PM  #1 
Senior Member Joined: Apr 2013 From: Ramallah, Palestine Posts: 349 Thanks: 0  Need someone to check my work what is the y intercept? y = 0 Is there any symmetry? yes odd because f(x) = f(x) so odd symettry On what intervals is the function increasing? (infinity,2)U(2,2)U(2,infinity) is it decreasing? It is never decreasing bc: when you plug in a 0 you get a 0 which is not negative, so it can't be decreasing. Where does the function have a local maximum? x = none because it is never decreasing Where does the function have a local miniomum? x = None because again it is never decreasing. Where is the function concave up? Take second derivative and get now i need to plug in two numbers a number smaller than the horizontal asymptote and one larger than the horizontal asymptote? but how do I know what they are? Like what Do i need to do at this point, cause i am kind of lost. Where are the inflection points? Again I need help 
October 23rd, 2013, 11:30 PM  #2 
Senior Member Joined: Oct 2013 From: Sydney Australia Posts: 126 Thanks: 0  Re: Need someone to check my work
I am really rusty on this stuff but g"(x) = 4x(x2)(x+2) This is a cubic finishing in the 1st and 3rd quadrants. When the function is concave up, g"(x) must be positive which happens when 2<x<0 and when x>2 When the function is concave down, g"(x) must be negative which happens when x<2 and when 0<x<2 So if concavity changes from negative to positive at a point doesn't that mean that the point is a point of inflection? And, since the function is never decreasing doesn't that mean that x=2,0, and 2 must all be points of inflection? Also, this is an odd function so it has point symmetry but it does not have an axis of symmetry. Like I said, I haven't done this stuff for a long time so maybe I am not right. Also, how do you put the maths type into your question? 

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