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Higher maths-nature table
Stuck on this question. I don't know what x could equal.
y=x to the power of 4 -2x squared +8.
I worked out that x= 0 or 2 or -2.
However, I can't work out how to draw the nature table. I suspect that I have done something wrong.
y=x to the power of 4 -2x squared +8.
I worked out that x= 0 or 2 or -2.
However, I can't work out how to draw the nature table. I suspect that I have done something wrong.
Anyone??
While i have no idea what you mean by a nature table (I don't do hippy maths) i'll try to help.
If the equation is x^4 - 2x^2 - 8 = 0 (*) then you can say t = x^2, and substitute it in getting t^2 - 2t - 8 = 0. Roots are then t = 2, t = -4. This then gives x^2 = 2, x^2 = -4
(*i changed equation to this because it didn't have complex roots, but then it does... check if you've copied the right equation please.)
So x = plus/minus root2, or plus/minus 2j
If the equation is x^4 - 2x^2 - 8 = 0 (*) then you can say t = x^2, and substitute it in getting t^2 - 2t - 8 = 0. Roots are then t = 2, t = -4. This then gives x^2 = 2, x^2 = -4
(*i changed equation to this because it didn't have complex roots, but then it does... check if you've copied the right equation please.)
So x = plus/minus root2, or plus/minus 2j
spex
While i have no idea what you mean by a nature table (I don't do hippy maths) i'll try to help.
If the equation is x^4 - 2x^2 - 8 = 0 (*) then you can say t = x^2, and substitute it in getting t^2 - 2t - 8 = 0. Roots are then t = 2, t = -4. This then gives x^2 = 2, x^2 = -4
(*i changed equation to this because it didn't have complex roots, but then it does... check if you've copied the right equation please.)
So x = plus/minus root2, or plus/minus 2j
If the equation is x^4 - 2x^2 - 8 = 0 (*) then you can say t = x^2, and substitute it in getting t^2 - 2t - 8 = 0. Roots are then t = 2, t = -4. This then gives x^2 = 2, x^2 = -4
(*i changed equation to this because it didn't have complex roots, but then it does... check if you've copied the right equation please.)
So x = plus/minus root2, or plus/minus 2j
The question is right. The topic it is in is Differentiation.
Ok, I may have done this completely wrong, so take what I say here with a pinch of salt!
y = x^4 + 2x^2 + 8
dy/dx = 4x^3 + 4x
= 4x(x^2 - 1)
x = 0 or x = 1
The nature table doesnt work with -1 because it's equal to zero (thinking i may have done it wrong). But if you do it with -2 it's negative. with 0.5 it's negative. and with 2 it's positive. So you get an answer of:
(0, 8) is a falling point of inflexion
(1, 7) is a minimum turning point (get the y-coord by substituting into your original formula.
I honestly don't know if this is right (in fact its probably not) but it's what i got!
y = x^4 + 2x^2 + 8
dy/dx = 4x^3 + 4x
= 4x(x^2 - 1)
x = 0 or x = 1
The nature table doesnt work with -1 because it's equal to zero (thinking i may have done it wrong). But if you do it with -2 it's negative. with 0.5 it's negative. and with 2 it's positive. So you get an answer of:
(0, 8) is a falling point of inflexion
(1, 7) is a minimum turning point (get the y-coord by substituting into your original formula.
I honestly don't know if this is right (in fact its probably not) but it's what i got!
I always got stuck on that last year!
just to determine nature & stationary points, u have to:
1. Differentiate equation
2. SP's exist when dy/dx=0 and solve this equation to get x and y coordinates
3. Determine nature of SP's - consider gradient of dy/dx on each side of SP by substituting values into differentiated equation
I know you didn't really want this, just the answer but it helped me anyway!
just to determine nature & stationary points, u have to:
1. Differentiate equation
2. SP's exist when dy/dx=0 and solve this equation to get x and y coordinates
3. Determine nature of SP's - consider gradient of dy/dx on each side of SP by substituting values into differentiated equation
I know you didn't really want this, just the answer but it helped me anyway!
What the hell's a nature table?
Can't you just do d2y/dx2 and throw the values in?
Also what is the equation because you've changed the coeffecient of x^2 from - to + and that gives two very different answers.
Can't you just do d2y/dx2 and throw the values in?
Also what is the equation because you've changed the coeffecient of x^2 from - to + and that gives two very different answers.
Slumpy
Second derivatives are advanced higher, all you'll need at higher are nature tables.
Nature tables confuse students needlessly and exercises involving them are tedious. Second derivatives are Advanced Higher, but there's no reason they can't be taught in Higher for this purpose in place of nature tables. They're far simpler.
Oogamy
Nature tables confuse students needlessly and exercises involving them are tedious. Second derivatives are Advanced Higher, but there's no reason they can't be taught in Higher for this purpose in place of nature tables. They're far simpler.
I never found anyone get particularly confused by nature tables.
If anything, second derivates are more confusing(especially if you don't understand why they should work, and moreso when they don't).
Either way, the case is, all the OP needs is a nature table, and thats what marks are given for in higher, as far as I remember examiners can be picky about people using things above the level they're at, even if it's right.
benwellsday
What the hell's a nature table?
Can't you just do d2y/dx2 and throw the values in?
Also what is the equation because you've changed the coeffecient of x^2 from - to + and that gives two very different answers.
Can't you just do d2y/dx2 and throw the values in?
Also what is the equation because you've changed the coeffecient of x^2 from - to + and that gives two very different answers.
this is higher - differentiation is covered but not second derrivatives
nature tables are a cheats way of doing second derrivatives
Oogamy
You should ask your teacher about finding the nature of stationary points by way of second derivative. Nature tables really are pointless.
is it a lot easier to drop marks using second derivatives than it is using nature tables - and only 1 mark will be given for finding the whole nature table generally so using second derivatives will take a lot of unnecessary time which a lot of people cant afford to do
in advanced higher you are given a few marks for second derrivatives and none for nature tables so it is sort of above the level that the OP needs to know just now
EDIT: sorry, thought you were english for a sec, dont mean to sound like im having a go
moonshine_1991
Stuck on this question. I don't know what x could equal.
y=x to the power of 4 -2x squared +8.
I worked out that x= 0 or 2 or -2.
However, I can't work out how to draw the nature table. I suspect that I have done something wrong.
y=x to the power of 4 -2x squared +8.
I worked out that x= 0 or 2 or -2.
However, I can't work out how to draw the nature table. I suspect that I have done something wrong.
the way i did it at higher was to say x=0 so 0^4-(2*0) + 8 was equal to 8 so positive
then x=2
and so on
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