Question

How do you find critical points? (get at least 2 of the 3 acceptable answers)

Answer 1

are you asking a method?

Answer 2

yeah, for example I know that you can find critical points by taking the derivative and setting it equal to zero, but what are the other possible ways?

Answer 3

You can plot a graph and then see the critical points - that's another method.

Answer 4

There's one more way, but I cant seem to get it. :/

Answer 5

yes..or plot on a sign diagram...(never liked that way)
for example, f(x)=(x-1)^2
factor out f(x)=(x=1)*(x-1), set x+1=0 set x-1=0.
these will be crit. points

Answer 6

oops..f(x)=(x+1)*(x-1)

Answer 7

So, to find critical points are you saying we just factor out the function and set it equal to zero (instead of taking the derivative?)

Answer 8

my mistake...been a while.
no done for first derivative...

Answer 9

are you trying to get the relative max and min, or also the absolutes?

Answer 10

For this question?

Answer 11

no..just trying to get context, since the 2nd der. will give absolutes

Answer 12

I'm sorry, Im confused.

Answer 13

well..me too.
you want 3 ways, in general, to find the critical values?

Answer 14

Yes.

Answer 15

the critical points are max, min and points of inflexion.

Answer 16

ok

Answer 17

ok. 2nd derivatives are the inflection points

Answer 18

1. Find the derivative and set it to 0. This way, you get max and min. The second derivative should give you points of inflexion.
2. Plot the equation on a graph and find the max, min and inflexion points visually.
3. Use a computer/calculator ;)?

Answer 19

calculator. hehehe

Answer 20

lol, maybe so. Thanks, guys (:

Answer 21

good luck