Question

How do I find the critical numbers of f' from the graph of f''?

Answer 1

I know how to find the critical numbers for the graph of f from f', but this is asking for the critical numbers of f' from f"", which I don't know how to do.

Answer 2

^*f"

Answer 3

if you know how to find the critical numbers of f with information from f', then
you can apply that same knowledge with the second derivative and apply it to f'...

put it this way...
let g=f'
then g' = f''

if you know the where g' is zero, that's the critical numbers of g...

Answer 4

RIght, I know that where ever x=0 on the graph of f', then those values are critical numbers of f. But how do I go about finding the critical numbers of f' just by looking at the graph of f''?

Answer 5

let f' = g, so f'' = g' ...
g' = 0 means f'' = 0.
so
"whereever g'=0 that's the critical numbers for g."
same statement:
"whereever f''=0 that's the critical numbers for f'."

Answer 6

So it's kind of the same process as finding the critical numbers of f from the graph of f''? The critical numbers of f' are where x=0 on f''?

Answer 7

*from the graph of f'

Answer 8

^type

Answer 9

*typo

Answer 10

exactly...

Answer 11

So since x=0 four times on the graph of f'', then there are four critical numbers of f'?

Answer 12

yes...

Answer 13

Ah. I guess I was just expecting the process to be different for second derivatives and such. Well thanks.

Answer 14

btw... you mean f''=0 four times on the graph, then there are four critical numbers of f'

Answer 15

Oh yes, that's what I mean. Thanks.

Answer 16

yw...)