Question

I've done some of the problem. I just need help with the rest. Will give a medal! (posting problem below)

Answer 1

\[f(x)= 5(\frac{1}{x-4}-\frac{1}{x+2})\]

Answer 2

I need to find the asymptotes, relative extrema, and inflection points of the function

Answer 3

So far I have solved for critical numbers and got: -2, 4, and 1

Answer 4

What should I do next?

Answer 5

@zepdrix
Are you good with calculus?

Answer 6

The critical points give you the asymtotes. For relative extremas you need to derivate the function, put the derivative to 0, then solve for x.

Answer 7

Maybe I didn't do something correctly? I took the derivative of the function and set the derivative equal to zero. The x values -2, 4 and 1. Aren't those the critical points?

Answer 8

I think only -2 and 4 are critical points, so x=1 can be an extrema.

Answer 9

Is there a way to tell that they are? Or do you just have to guess?

Answer 10

@math&ing001

Answer 11

No sorry, you're right critical points are -2, 4 and 1. It's all points that verify f'(c)=0 or f'(c) doesn't exist. Here -2 and 4 don't exist so they are asymptotes, and 1 is a local extrema.

Answer 12

Ah, thank you for the clarification.
So unrefined = asymptote and 0 = extrema?

Answer 13

Yeah ! Back in high school we used to make this really useful table:

Answer 14

Thank you for the table. I'll save it, and keep it for future use.

Answer 15

By the way if I opened up another question, do you think you could help me with another calculus problem?

Answer 16

Sure !