HOW DO I FIND THE INFLECTION POINT from the function y=x^4-8x^3-16x+5 PLEASE HELP THANKS

Question

anonymous · Answer

I got the second derivative it is 12(x-4)

anonymous · Answer

@dan815 can you help man?

anonymous · Answer

I feel as if there aren't any

anonymous · Answer

attachment

anonymous · Answer

As you said you get :
$$f''(x)=12(x-4)$$
We remark thet 
$$f''(4)=0$$
and f'' is negative before 4 and positive after 4, i.e f'' change its sign at 4
So (4,f(4)) is an inflection point of the graph of the function !
Calculate f(4) ;)

anonymous · Answer

I get an insane number

anonymous · Answer

-315

anonymous · Answer

am I doing this correctly? For some reason this is so challenging

anonymous · Answer

Whatever ! The important point is :
to find an inflection point you need to calculate f'' and finding the numbers a such that :
$$f''(a)=0$$
and the sign of f'' changes at a ;)

anonymous · Answer

ok! and I have to graph this function and it is concave up for the entire thing

anonymous · Answer

The sign of f'' decides if the graph is concave up or down ;)

anonymous · Answer

My points seem like they are all over the place oh well ughh

anonymous · Answer

are you good with horizontal and vertical asymptotes?

anonymous · Answer

go ahead !

anonymous · Answer

I need the vertical + horizontal asymptotes for f(x)=2x^2+7x-15/5x+x^2