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October 23rd, 2013, 11:10 PM   #1
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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
Shamieh is offline  
 
October 24th, 2013, 12:30 AM   #2
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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 -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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