Newton's Method

Hi
Does anyone know how to use Newton's Method to do , say, find the absolute minimum of 1/4*x^4+x^2+5x ?
thanks

Isn't that a quadratic equation?

I thought that the A level method of solving it applies??

Vince

Newton's method is not required.

y = (x^4)/4 + x^2 + 5x

dy/dx = x^3 + 2x + 5

maximum/minimum when dy/dx = 0

Therefore x^3 + 2x + 5 = 0

Using graphics calculator :

x = -1.328268856... (only real root, 2 other roots with imaginary parts)

If an exact result is required, there is a formula for cubic equations in the same way that for the quadratic equation ax^2 + bx + c = 0,
x = (-b +/- (b^2 - 4ac)^0.5)/2a

d2y/dx2 = 3x^2 +2, which is always >0, so point is a minimum.

PS Yes I know this because i did A Level Maths and Further Maths this year.

Excuse me, but that's not the quadratic formula.

There's no "^-1" in there, only "^1/2"

Quote:

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Originally posted by alkatran
Excuse me, but that's not the quadratic formula.

There's no "^-1" in there, only "^1/2"

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Indeed, x^0.5 is the equivalent of taking the square root of x.

Quote:

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Originally posted by alkatran
Excuse me, but that's not the quadratic formula.

There's no "^-1" in there, only "^1/2"

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Sorry, my mistake

Used to just writing a square root sign but there isn't one on my keyboard.