Absolute maximum

[Matt]

Hello All

Can some one please show me how to find the absolute maximum (x & y)
from a 4th order polynomial equation...

Excel tells me the equation is;
Y=-0.007x³+0.0321x²-0.4409x+3.6696

The equation was derived from the following x,y points;
(12.27,1.721),(14.43,1.762),(17.03,1.808),(19.22,1.790)

I know the absolute maximum is approx (17.6,1.810) by physically
graphing and then reading of the max point but is there any way Excel
can calculate this for me?

Any thoughts appreciated, thanx in advance

Matt

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[Ron Rosenfeld]

Hello All

Can some one please show me how to find the absolute maximum (x & y)
from a 4th order polynomial equation...

Excel tells me the equation is;
Y=-0.007x³+0.0321x²-0.4409x+3.6696

The equation was derived from the following x,y points;
(12.27,1.721),(14.43,1.762),(17.03,1.808),(19.22,1.790)

I know the absolute maximum is approx (17.6,1.810) by physically
graphing and then reading of the max point but is there any way Excel
can calculate this for me?

Any thoughts appreciated, thanx in advance

Matt

I don't know if there is a formulaic solution. However, you could use Solver
to derive a solution.

First you put the formula into a cell, and I would reformat the formula to a
maximum number of significant digits:

= -0.000739375705996*x^3 + 0.032062064793544*x^2
- 0.440893080397058*x + 3.66955823485892

Then use Solver to vary 'x' to get a maximum value.

The numbers I come up with are:

x = 17.642996928978300
y = 1.810487517581320




--ron

 

[Dana DeLouis]

On could take the derivative and solve for zero. If your coefficients are
{a,b,c} =

-0.00073937571, 0.032062065, -0.44089308

Maybe you could solve the "Local" max and min with these..
(-b - Sqrt(b^2 - 3*a*c))/(3*a)
(-b + Sqrt(b^2 - 3*a*c))/(3*a)

Using
(-b - Sqrt(b^2 - 3*a*c))/(3*a)
I get:
17.64302992747007