Let f be the function defined by f(x)=x^2 +x and divide the interval [-1,2] into six subintervals of equal length.

I am having trouble finding what those subintervals should be. Can someone please show me how you would find them?

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- March 11th 2010, 04:15 PMsummerset353partitions
Let f be the function defined by f(x)=x^2 +x and divide the interval [-1,2] into six subintervals of equal length.

I am having trouble finding what those subintervals should be. Can someone please show me how you would find them? - March 11th 2010, 04:53 PMmabruka
Well hmm, i'll give you an idea you do the rest.

Say we want to give a partition of [0,2] in 7 subintervals of equal length.

First you need to know the length of the the original, in this case it would be 2.

So if i want to divide it in 7 parts, each part needs to have length: 2/7

So... the partition would be:

[0,2/7],[2/7,4/7],[4/7,6/7],[6/7,8/7],[8/7,10/7],[10/7,12/7],[12/7,14/7]=[12/7,2]

What about your interval?

(Obs: The function f plays no role in finding a partition of equal length, UNLESS you need something else like piecewise-continuous or what ever.)