HellVeN
Banned
- Joined
- Jun 26, 2004
- Messages
- 532
- Gender
- Male
- HSC
- 2005
Whilst revising, I came across a question where using y'' to find the nature of a stationary pt didn't work. Now I know I could just have found its nature by using by testing y' of LHS and RHS but I was wondering why the method that uses y'' didn't work?
And If it doesn't work iss it safer to always use the testing y' LHS and RHS method?
The question was this:
Find the stationary point on the curve y = (3x^4)+1 and determine what type of point it is.
I did this the y'' way and it doesn't work...
y = (3x^4)+1
y' = 12x^3
y'' = 36x^2
.:. for stationary pts y'=0
12x^3 = 0
x = 0
Now y'' = 36*0^2 = 0
So now I'm thinking this fucker's a possible horizontal pt of inflexion, and i test it and it comes out that LHS is + and RHS is + , therefore concativity doesn't change and I'm fucked.
The answer says it's a minimum and I knew this cause its an x^4 but WHY doesn't the method above work? Shouldn't I have gotten y'' > 0 for a minimum st point?
And If it doesn't work iss it safer to always use the testing y' LHS and RHS method?
The question was this:
Find the stationary point on the curve y = (3x^4)+1 and determine what type of point it is.
I did this the y'' way and it doesn't work...
y = (3x^4)+1
y' = 12x^3
y'' = 36x^2
.:. for stationary pts y'=0
12x^3 = 0
x = 0
Now y'' = 36*0^2 = 0
So now I'm thinking this fucker's a possible horizontal pt of inflexion, and i test it and it comes out that LHS is + and RHS is + , therefore concativity doesn't change and I'm fucked.
The answer says it's a minimum and I knew this cause its an x^4 but WHY doesn't the method above work? Shouldn't I have gotten y'' > 0 for a minimum st point?