Question

Find the extreme values of the function and where they occur

Answer 1

\[1/(x^2-1)\]

Answer 2

@Loser66

Answer 3

What is the definition of extreme value?

Answer 4

The relative (or local) max/min points.

Answer 5

yes, so that just take derivative of f

Answer 6

Only 1 derivative?

Answer 7

let it =0, find x
replace that x into the original function, and you are done.

Answer 8

first derivative only.

Answer 9

Oh! So when i write the answer i just say y=??

Answer 10

When you get the result (x =0) , your conclusion is
f(x) has extreme value and x =0 and f(0) = -1

Answer 11

*at, not and
f(x) has extreme value AT x =0 ,....

Answer 12

ohh, okay, let me solve it.

Answer 13

\[f'(x)=\left(\begin{matrix}-2x \\ (x^2-1)^2\end{matrix}\right)\]

Answer 14

correct?

Answer 15

It is NOT a matrix, it is a fraction. but it is correct.

Answer 16

yeah sorry, meant to be a fraction

Answer 17

so how do i solve for x from here?

Answer 18

you solve for f' =0 iff the numerator =0

Answer 19

and the numerator is -2x =0 iff x =0, right?

Answer 20

correct

Answer 21

so x=0?

Answer 22

plug back to original one to find value of f(0)=??

Answer 23

-1?

Answer 24

yup

Answer 25

So the answer doesn't have to be like, absolute max = ??
absolute min= ??

Answer 26

sorry just making sure haha

Answer 27

If you have 2 solutions, plug back and compare which one is larger, the larger one is max, the lesser one is min
In this case, you have only 1 solution. You have no comparison, how to say whether it is max or min?

Answer 28

this is sketch of f(X)
so x=0 is not abs max