Help!! (1 Viewer)

[tinaxo.]

When finding stationary points and determining their nature, how do you know which to use - first or second derivatives?

Thanks =)

 

[Timothy.Siu]

to get stationary points, you use the first derivate and solve for y'=0 which would give you the x coordinate for the stationary point, then you can sub that into the y equation to find the y coordinate.

to determine the nature, you can use the second derivative and sub the x value for the stationary point into it. if y''<0 when subbed in, the it is a max. turning pt. if its >0 then its a minimum turning point, and if y''=0 its an inflexion pt. (not sure if thats always true someone confirm this, u might have to test it?)

 

[oly1991]

to get stationary points, you use the first derivate and solve for y'=0 which would give you the x coordinate for the stationary point, then you can sub that into the y equation to find the y coordinate.

to determine the nature, you can use the second derivative and sub the x value for the stationary point into it. if y''<0 when subbed in, the it is a max. turning pt. if its >0 then its a minimum turning point, and if y''=0 its an inflexion pt. (not sure if thats always true someone confirm this, u might have to test it?)

when y''=0, yes you have to test LHS and RHS to see if concavity changes. If it does, then it is a "horizaontal inflexion".

 

[tinaxo.]

Thanks.

I tested this method with ALOT of questions and it worked with each one. I really appreciate the help.