Maths Question (1 Viewer)

[Kabeio]

I need help with this question!!

Supposed y = 2x ³ + 3x² -12x + 8

How would i find the coordinates of stationary points and the nature of the stationary points and points of inflexion and then draw it?

Thanks!!!

 

[Slidey]

Stationary points are always found by deriving and letting the derivative equal zero.

y'=6x^2+6x-12=0
x^2+x-2=0
(x+2)(x-1)=0
Stationary points at x=1 and x=-2

Nature of stat points is found by taking second derivative and substituting the x value into this:
y''=12x+6
y''(1)=18>0 .'. concave down
y''(-2)=-18<0 .'. concave up
Points of inflexion are found by taking the second derivative and letting it equal zero, so:
y''=12x+6=0
x=-1/2 is a POSSIBLE point of inflexion.

The only way I know to test for points of inflexion is to take derivatives past the second one. In this case, y'''=12 > 0 so there is a point of inflexion at x=-1/2.

 

[Kabeio]

lol ok then, thanks anyway


Anybody else??

 

[Slidey]

Have you tried looking at your textbook?

 

[Adrian.]

The only way I know to test for points of inflexion is to take derivatives past the second one. In this case, y'''=12 > 0 so there is a point of inflexion at x=-1/2.

Another way to test is to make x A little less and then a little greater than -1/2 and test those in y''. If they're both concave up or concave down then it's not a pt. of inflexion. If one is concave up and one is concave down it is a point of inflexion.

It's been a while since I've done calculas so maybe wait until someone else confirms what I've said, or do what Sliderule or your textbook says.

-Edit- Slide, what is photovoltaics?

-Edit 2- Add the new values to y'' not y'

 

[Slidey]

I tried that and ended up with no point of inflexion.

Photovoltaics is the study of solar energy and solar cells. It involves quantum mechanics, some chemistry, a fair amount of maths. It's in a way like electrical engineering, but applied to solar cells.

I've added some links to my sig, so... check them out.

 

[Adrian.]

Sorry, you add the new values to y''. My bad

Like this:

y'' =12x + 6
y'' (-0.45) = 0.6 (Concave up)
y'' (-0.55) = -.0,6 (Concave down)

Therefore x=-1/2 is a point of inflexion.


Thanks I'll take a look at the links.

 

[AntiHyper]

y = 2x ³ + 3x² -12x + 8

How do you get the squared and cubed symbols?

 

[Xayma]

To get the symbols (sup)2(/sup) replacing ( ) with either [ ] or < > depending on if HTML or vB code is on. It is probably better to use [ ] since it is on every forum, but I prefer < > cause Im use to it and I can get more mathematical symbols with it.

The only way I know to test for points of inflexion is to take derivatives past the second one. In this case, y'''=12 > 0 so there is a point of inflexion at x=-1/2.

Try testing the concavity either side of the point of inflexion. In a fair few circumstances, this will be quicker if you only have one or two possible points of inflexion, particularly if the second derivative is a fraction.

Ie test the concavity at x=-1/2-&delta;x and x=-1/2+&delta;x

 

[nit]

Yep, use a table of slopes using the 2nd derivative to test for concavity and, at the same time, points of inflexion.

 

[Slidey]

Figures. I was testing x+ an infinitesimal in y'.

Ah well, I'll remember for next time.

 

[AntiHyper]

Ohh..
Test: ^23dsa

I guess then (sdown)(/sdown) is for subscripts
Test: [sdown]23dsa[/sdown]

 

[Xayma]

No. (sub)(/sub)

 

[Slidey]

Try (sub)(/sub)

sup stands for superscript, sub stands for subscript.

 

[Jago]

press and hold alt, then press 0, 1, 7, 8 for ²

and 0, 1, 7, 9 for ³

 

[shannonm]

slidey why is there a link to unsw pv in your sig