# Finding the mix and max of this quartic function?Watch

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#1
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!
0
5 years ago
#2
(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!
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?
0
5 years ago
#3
(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.
0
#4
I can solve cubic, it's just a case of getting there
0
5 years ago
#5
(Original post by Epel.dh)
I can solve cubic, it's just a case of getting there
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!
0
5 years ago
#6
(Original post by Epel.dh)
I can solve cubic, it's just a case of getting there
So the cubic equation you are trying to solve is:

Over to you.
2
5 years ago
#7
The function does have 3 stationary points and 2 points of inflection.

if you equate the first equation to zero, multiply by you get the "simplified"

(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.)
0
5 years ago
#8

EDIT (kudos, Mr M)
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