Thread: partitions

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?

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.)