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When dealing with cubics (ax^3 + bx^2 + cx +d) are there plug and chug formulas avalible to find:
1) Max and Min values (ie the turning points of the graph)
and
2) The area under the curve
Right now I have about 30+ cubic equations that I have the coefficients for but need to find 1 and 2. I dont want to go through each one by taking the derivitives etc ... I am just wanting to set something up in Excel where I can place the coefficients in certain columns and I will recieve the results for 1 and 2 automatically.

Any ideas??

Any and all help wanted.

Thanks in advance :)

2006-10-04 16:51:17 · 3 answers · asked by ??Math?? 2 in Science & Mathematics Mathematics

3 answers

1.
Derivatives are the way to go. If you want to set up something in Excel, you'll need to set up the derivative formula. The derivative formula *is* your "plug and chug" formula, there's really no good way around it.

2.
For the area under the curve, I really don't think there's any good shortcut either. You just have to integrate. Of course, if you're dealing with polynomials (so you don't have to integrate weird stuff like trig functions), setting up the formula in a spreadsheet wouldn't be any harder than setting up the formula for derivatives.

Sorry if this doesn't help much. It sounds like you know what you need to do, but you just aren't looking forward to grinding through all those formulas. Unfortunately, you pretty much have to do it.

2006-10-04 17:10:05 · answer #1 · answered by Bramblyspam 7 · 0 0

Just solve the problem in general and put the results into Excel. First take the derivative of the general cubic:

d/dx (ax^3 + bx^2 + cx +d) = 3*a*x^2 + 2*b*x + c

You want to evaluate this at zero. This is just a quadratic:

3*a*x^2 + 2*b*x + c = 0

Solve this with the quadratic equation:

x = (-2*b +- sqrt(4*b^2 - 12*a*c))/(6*a)

x = (-b +- sqrt(b^2 - 3*a*c))/(3*a)

That gives you the x value for the max and min. Find these 2 x values and put them into the original cubic. Pretty straightforward in Excel.

The integration is similar, just do it in the general case. You didn't say what the limits of integration are, but those too should be solveable in closed form.

2006-10-04 18:21:06 · answer #2 · answered by Pretzels 5 · 0 0

for max and min you need to get the derivative and let it equal to zero. you will have 2 answers, when u put them in the initial equation, it will be the Max and Min.

the area under curve is integral. so u have to get the integral over the demanded area, that will give u the answer.

ALSO if you dont want to get the derivative and integral, there's an algebraic equation which is the definition of derivative and integral, which you can enter them into excel and get the result :)

2006-10-04 17:05:49 · answer #3 · answered by alwayss_ready 3 · 0 0

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