Turning point

[Ilovemathsmeth]

OR

[brightsky]

Ahh ok, thanx. What does the ______mean? And the 'signs' are the direction of which the graph is going at that point right? Like a tangent to the point?

[brightsky]

OR

+1

[Ilovemathsmeth]

Ah that represents linear equations - like for a positive linear graph, the line slopes from left to right etc and it's ___ because it's a horizontal line that gives zero gradient.

[brightsky]

So how do you use it to find out if it is a point of inflexion or a turning point? Soz, me's a bit slow..:p

[Hielly]

So the TP for



dy/dx=0

x-2 is a factor

then i used division of polynomials and got,



so x=2,-1/3 and 5/6

when rechecking with calc, i plugged the orignal equation into the calc it says the x=2,-1/3

Not sure what i did wrong.

Thanks

[kamil9876]

not all points at which dy/dx=0 are turning points. But all turning points (at least for functions enountered in VCE) have dy/dx=0. THat is why we solve dy/dx=0 first, and then we know that every turning point will be one of those values, but not all those values have to neccesarily be turning points. To distinguish between which are and which are not, use the method Ilovemathsmeth posted.  

[brightsky]

You're calculator must be wrong (lol! oh the irony...) In a quartic, there should be 3 turning points, and no points of inflex (am I wrong here?) Are you sure you entered the right equation into the calculator? All three of your x-values are x-coordinates for turning points on the quartic, with 2 being local minimums and 1 being local maximum.

[kyzoo]

not all points at which dy/dx=0 are turning points. But all turning points (at least for functions enountered in VCE) have dy/dx=0. THat is why we solve dy/dx=0 first, and then we know that every turning point will be one of those values, but not all those values have to neccesarily be turning points. To distinguish between which are and which are not, use the method Ilovemathsmeth posted. 

True but that's why you back it up with a calculator graph, your knowledge of the graph's general shape, or one those tables with gradient values and graph appearance (sorry, dunno what's it's called =( )

[Ilovemathsmeth]

So how do you use it to find out if it is a point of inflexion or a turning point? Soz, me's a bit slow..:p

If you've got two lines sloping in the same direction with a horizontal line in between, it's a stationary point of inflexion. I.e. the gradient is the same either side of the point of zero gradient.