1. ## Critical point? Help me please

Hello i have a test tomorrow and i can't figure this out.

I need to find the critical points, local extrema, intervals of decrease and increase, intervals of concavity, inflection point, and the vertical and horizontal asymptotes.

for this equation

f(x)= x/((x^2)-9)

Any help at all would be great, thanks

2. Originally Posted by bdavidson
Hello i have a test tomorrow and i can't figure this out.

I need to find the critical points, local extrema, intervals of decrease and increase, intervals of concavity, inflection point, and the vertical and horizontal asymptotes.

for this equation

f(x)= x/((x^2)-9)

Any help at all would be great, thanks
Do you know how to find the derivative?

Do you know the relationship between the derivative and "critical points, local extrema, intervals of decrease and increase, intervals of concavity, inflection point"?

Horizontal aymptote is y = 0 (why?). Vertical asymptotes found by solving x^2 - 9 = 0 (why?)

3. Originally Posted by bdavidson
Hello i have a test tomorrow and i can't figure this out.

I need to find the critical points, local extrema, intervals of decrease and increase, intervals of concavity, inflection point, and the vertical and horizontal asymptotes.

for this equation

f(x)= x/((x^2)-9)

Any help at all would be great, thanks

1.Take the derivative(use the Quotient Rule)
2.Find the critical points by setting f'(x)=0, and solve for x
3.Use the little table thing, plug in the points to find the interval of dec&inc
4.Take the second derivative
5.Same thing as #3, but to find the concavity
6.Inflection point, I believe you get al lthe points from the second derivative, and find it by plugging it into the original function. (x, f(x))
7.Guy above me said it

4. for the vertical asymptote solve this equation:

x^2-9=0;

for horizontal asymptote the solution is like this:

$\displaystyle \lim_ {x\to\infty}f(x)$