Question

I have a doozie. I am asked to find some graphing behaviors but before I even get there, I have to derive e^x/(x^2-9). f'(x), I found, equals (e^x(x^2-2x-9))/(x^2-9). But I can't find f''(x).

Answer 1

Okay, I have my f''(x)! Now I need to find my behavior of f(x)'s graph based on what I can infer from my graphs of my first and second derivative. Can anyone give me a hand finding concavity?

Answer 2

Here's my f''(x): (e^x(x^4-2x^3-16x^2+18x-99))/(x^2-9)^2

I got one of my critical points as the DNE of the denominator equaling +/-3, when you set it to zero.

Answer 3

I can't solve the numerator when I set it to zero, how should I go about solving it?

Answer 4

okay, so e^x can't equal zero!

Answer 5

Comparing your f''(x) with the one I got from WolframAlpha, I think you made a mistake along the way...

Answer 6

ugh, where?

Answer 7

I'm not sure. The x^4 term is correct, all the others are different :-)

Answer 8

http://www.wolframalpha.com/input/?i=derivative+%28derivative+e%5Ex%2F%28x%5E2-9%29%29

Answer 9

no, I'm looking at my Wolfram Alpha result, it seems right.

Answer 10

Crud, you're right

Answer 11

Okay, I think I have to call this quits for the evening. I've put hours into this and haven't gotten anywhere. G'night.

Answer 12

Thank you, btw, whpalmer4

Answer 13

It's weird, I had a window that I could have sworn had a different polynomial in the numerator, but now I can't find or replicate it, I keep getting what you've got...

Answer 14

Yeah somewhere along the line I or you entered something the wrong way. Lots of ^'s and parentheses.

Answer 15

Ah, maybe this was it: http://www.wolframalpha.com/input/?i=derivative+%28derivative+e%5Ex%2F%28x%5E2-9%29%29

Answer 16

Well, work it both ways, pick the one you like better :-)

Answer 17

I think the denominator is squared

Answer 18

remember, it's the second derivative, I had to use the product rule, then the quotient rule ((f'g)-(g'f))/g^2

Answer 19

I think you left off the ^2 on your Wolfram Alpha entry?

Answer 20

I think my usefulness for the night has been exhausted, and I don't want to be sending you on any wild goose chases, so I'll just good night and good luck!

Answer 21

Sames, I'm sure we're both off a little. Thank you for attempting to help where no one else has dared. I appreciate it.

Answer 22

You were right! I had to do a product rule of my denominator before I could plug it in to my quotient rule and that gave me what Wolfram gave me. The graph doesn't look right, but my assignment is due in 30 mins so from here on out, it'll be fate that determines my concavity.

Answer 23

Let us all bow and give prayerful thanks to our patron saint, Stephen of Wolfram, for he leads us through the thickets to salvation :-)