Question

find the critical numbers of f if any and locate all relative extrema. f(x)=x/x+1

Answer 1

Critical points are just points in f(x) when f'(x) = 0, basically you are finding the roots of the derivative and plugging the x values back into your function.

What's in your way? Do you know how to take a derivative? Do you know how to find roots?

Answer 2

i know how to find the derivative i just get stuck on finding the roots for this problem

Answer 3

Okay, what is your derivative?

Answer 4

i got 1/(x+1)^2

Answer 5

Okay so we have:\[\frac{1}{(x+1)^2}=0\]Make sense?

Answer 6

yeas

Answer 7

Okay, so first we can multiply both sides by \((x+1)^2\).

Answer 8

What you get?

Answer 9

u mean multiply (x+1)^2 on both sides of the equation?

Answer 10

wait... right that doesn't work does it...

Answer 11

nope

Answer 12

Well we might now have any roots...

Answer 13

not have any?

Answer 14

yeah, looks like there aren't any... since you can't get the left hand side to be 0.

Answer 15

okay so then how do i proceed w. this problem?

Answer 16

Well, it seems like there are no critical points, so I would assume there are no relative extrema