first derivative test

once you have found the stationary points of a deivative to do first derviative test do you put this in to your orignal function so for eg

if one stationary point was -2 you choose xl to be -3 and xr to be -1

your function is 3x⁴- 2x² - 5x²+ 3

do you work your way through the equation replacing x with - 2 and x with -1 to find wheather the function is going to be a local minimum or maximum

thanks in advance

Reply 1

joostan

13

Original post by zamzam

once you have found the stationary points of a deivative to do first derviative test do you put this in to your orignal function so for eg

if one stationary point was -2 you choose xl to be -3 and xr to be -1

your function is 3x⁴- 2x² - 5x²+ 3

do you work your way through the equation replacing x with - 2 and x with -1 to find wheather the function is going to be a local minimum or maximum

thanks in advance

If you mean -3 and -1 then yes you sub into f'(x) :smile:

A quicker method is to take the second derivative if you've done that?

(edited 11 years ago)

Reply 2

claret_n_blue

17

-3 and -1, yes.

If the sign changes from positive to negative, then you have a local maximum.

If the sign changes from negative to positive, then you have a local minimum.

EDIT: Didn't read the question properly. Sorry.

Like ghostwalker said, you put it in the function for your derivative. The signs will show the gradient. So going from negative to positive means that your function was decreasing, stops changing gradient (at your stationary point) and then starts increasing and so that's why your stationary point would be a local minimum.