Question

Find the extrema and points of inflection for f(x) = 3x / (x+8)^2

Answer 1

\[3x / (x+8)^{2}\]

Answer 2

so to do that yo will need to take the first derivative!

Answer 3

I never remember the quotient rule off the top of my head so I will improvise.. haha

Answer 4

dtop(bottom)-d(bottom)top=0 rtemeber you dont need to do bottom squared and set that equal to 0 because at 0 its undefined ;)

Answer 5

f(x) = 3x * (x+8)^(-2) and just use the chain rule

Answer 6

f '(x) = 3x * (-2)(x+8)^(-3) + (x+8)^(-2) * 3

Answer 7

no this would be product rule not the chain

Answer 8

woops sorry meant product and chain rules..

Answer 9

Don't bother, bahrom7893, I've got it here (points to head). The problem is that with all my homework problems, I've been getting the wrong answer somehow. This was the same stuff I was nailing on my test last Friday, but it's coming out WRONG on homework?

Quotient Rule: f(x) g'(x) - f'(x)g(x) / g(x)^2

Answer 10

ohh do u just want the answer?

Answer 11

if it's OK, I'd prefer that you guys watch the steps I take and let me know if I mess up.

Answer 12

That is if you have some free time...

Answer 13

shoot

Answer 14

then ill continue:
f '(x) = 3x * (-2)(x+8)^(-3) + (x+8)^(-2) * 3
f'(x) = [-6x/(x+8)^3] + [3/(x+8)^2]

Answer 15

okay from now on typing is going to be a pain in the asymptote so let's just go on twiddla..
http://www.twiddla.com/575500

Answer 16

It would take too long to write it out. For the first derivative, i got

-3(x+16) / 2(x+8)^3

Answer 17

bahrom7893 is getting -3(x+8)...I'm about to give up. LOL

Answer 18

3x / (x+8)^2

f'=3(x+8)^2-(2(x+8)(3x)/(x+8)^4=0

(x^2+16x+64)-2x^2-16x=0
-x^2+64=0
(x-8)x(+8)=0
x=+-8

Answer 19

So I shouldn't convert it to (x+8)^-2 for f(x) and use the product rule? Stick with the layout given by the problem (requiring quotient rule)?

Answer 20

then take the f'' which looks nasty and i dont want to do it but its the same as the first part i did those numbers extrema and the f'' are either positive or negative and those are the concave up or down

Answer 21

NOOOOOOOOOO yes use quoetient rule

Answer 22

but at -8 its undefined so +8 is the max or min depending on f''

Answer 23

for f'' you have to test numbers around the one that =0 remeber to see if it goes -,+,- so its concave down

Answer 24

to do a simple one f(x)=x^3
f'=3x^2=0 x=0 so thats a min or max
f''=6x=0 x also is 0

test-100,100 and at f''(-100) you get <0
f(100)=>0 so at 0 you get a min which is concave up which is exactly what you see in the graph

Answer 25

seems i've been wasting time on twiddla... explaining all that to nobody..