Question

Find the local max and min for the below equation.

Answer 1

\[f'(x)=\frac{ -(x+1) }{ (x-1)^3 }\]

Answer 2

The function's extrema (max/min), occur when f'(x) = 0 or when f'(x) does not exist.

Answer 3

In your case, when does f'(x) = 0?

Answer 4

when f equals 1 and -1

Answer 5

no, only when x equals -1.

Answer 6

That's how you end up with -(-1+1) = 0 on top.

Answer 7

when finding the local max and min, you're only dealing with the numerator?

Answer 8

No, that's not the point, you're dealing with the entire function of the derivative.

Answer 9

ic, so you have to plug the answer back into the function and see which one has an output?

Answer 10

The thing is, a fraction is 0, IF AND ONLY IF the numerator is 0.

Answer 11

i kind of don't get it. what does a fraction have to be 0

Answer 12

So, you have a relative max/min at x = -1. Now 2nd part: a function can also have a relative max/min when the 2nd derivative doesn't exist.

Answer 13

why does*

Answer 14

Because your f ' is a fraction.

Answer 15

ah. so i have to find the 2nd derivative and do the same steps as finding it for the first derivative?

Answer 16

Sorry, my statement above was wrong:
Now 2nd part: a function can also have a relative max/min when the 2nd derivative doesn't exist.
I meant to say:
Now 2nd part: a function can also have a relative max/min when the 1st derivative doesn't exist.

Answer 17

oh derp. okay. so my min/max is -1,0

Answer 18

now how do i determine if it is an max or min?

Answer 19

That's not the whole thing, remember. Slow down. The function also has a relative max/min when the first derivative does not exist. For what values of x does this not exist?
\[\frac{ -(x+1) }{ (x-1)^3 }\]

Answer 20

x=1

Answer 21

correct. So you have two extrema at x=-1, and at x=1. Now, to determine whether they are max or min: