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 October 23rd, 2013, 11:10 PM #1 Senior Member   Joined: Apr 2013 From: Ramallah, Palestine Posts: 349 Thanks: 0 Need someone to check my work $g(x)= 1/5x^5 - 8/3x^3 + 16x$ 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? $x^4 - 8x^2 + 16 = 0 (x^2 - 4)(x^2 - 4) = 0 x +- 2$ (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 $g''(x) = 4x(x^2 - 4)$ 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 24th, 2013, 12:30 AM #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(x-2)(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 -22 When the function is concave down, g"(x) must be negative which happens when x<-2 and when 0

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