Calculus/Calc

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Expert: - 9/7/2010


Question
how do i solve -3x^3+x+4=2.05

Answer
I would solve it using Excel.
Note that this is the same as 3x^3-x-1.95=0.
In A1 put a guess for x
In B1 put =3*A1^3-A1-1
in A2, put another guess for x
In B2, copy B1
In C2, put =(B2-B1)/(A2-A1)
In A3, put =A1-B1/C2
In B3 copy B2, in C3, copy C2

Now, copy A3:C3 down.
That is, column A is x, column B is y, and column C is the slope.
I get
0   4   
1   2   -2
2   -18   -20
1.1   1.107   -21.23  for the elements with no format.

with no format for the first two rows and then
1.152143194   0.563961262   -10.41437435
1.206295392   -0.059721657   -11.51722261
1.20110997   0.002711451   -12.04012146
1.201335171   1.20934E-05   -11.98642101
1.20133618   -2.46747E-09   -11.98886665
1.20133618   0

The solution would be the first element in the last row since that is the x value that gives a 0 y value.

Now there is some fancy way of solving a cubic, so to see it:
http://en.wikipedia.org/wiki/Cubic_function

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