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Finding the mix and max of this quartic function?

Hi!

I've been trying to find the min and max values of this polynomial function;

y = 3x10-8x4 - 8 x 10-6x3 + 0.0001x2 + 0.0415x + 4.7

I have the values from using WolframAlpha but would like to know how to get there myself, although I've absolutely no idea how. Is there a standard method I could try and post my progress? Thank you! :smile:
Original post by Epel.dh
Hi!

I've been trying to find the min and max values of this polynomial function;

y = 3x10-8x4 - 8 x 10-6x3 + 0.0001x2 + 0.0415x + 4.7

I have the values from using WolframAlpha but would like to know how to get there myself, although I've absolutely no idea how. Is there a standard method I could try and post my progress? Thank you! :smile:


Did you try equating the first differential to 0 to find the stationary points (as the gradient of a SP should be 0), then substituting these coordinates into the second differential?
Original post by TheGrinningSkull
Did you try equating the first differential to 0 to find the stationary points (as the gradient of a SP should be 0), then substituting these coordinates into the second differential?


I presume the OP doesn't know how to solve cubic equations.
Reply 3
Avatar for Epel.dh
Epel.dh
OP
I can solve cubic, it's just a case of getting there :confused:
Original post by Epel.dh
I can solve cubic, it's just a case of getting there :confused:


In that case, what've you tried? And getting where specifically?

Finding the first differential of the equation gives you the gradient of the function. If this gradient is 0, you know it's a stationary point, as it's flat.

So now you have a cubic equation!
Original post by Epel.dh
I can solve cubic, it's just a case of getting there :confused:


So the cubic equation you are trying to solve is:

3x3−600x2+5000x+1037500=03x^3 - 600x^2 + 5000x + 1037500 = 0

Over to you.
Reply 6
Avatar for Hasufel
Hasufel
16
The function does have 3 stationary points and 2 points of inflection.

if you equate the first equation to zero, multiply by 10810^{8} you get the "simplified"

3x4−800x3+10000x2−4150000x+470000000=03x^{4}-800x^{3}+10000x^{2}-4150000x+470000000=0

(at this point, the coefficient of x^4 is +ve, so you`re looking at 2 minimums and a maximum - the classic "W" shape)

you can derive the above and use a numerical method (e.g. Newton-Raphson) to find the "roots" (i.e. stationary points), but you need 3 good starting points or "guesses"

(to find the inflection points is easier - derive again and you have a quadratic you can solve using the quadratic formula to get the inflection points.)
Reply 7
Avatar for Hasufel
Hasufel
16
follow Mr M`s lead...(and Maybe Mr Newton`s as well)

EDIT (kudos, Mr M)
(edited 10 years ago)

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