Use triangle ineq. to find a value of M such that...

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leoduong

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use the triangle inequality to find a value of M such that
|x^3 - 2x + 1| < M
for all x in the interval (-2,3).
 
Re: find a value of M such that...

I am guessing that they're looking for the least value of M that you can find. You can split this up as |x[sup:1mmzj4cu]3[/sup:1mmzj4cu]| + |-2x + 1|, |x[sup:1mmzj4cu]3[/sup:1mmzj4cu] + 1| + |-2x|, or |x[sup:1mmzj4cu]3[/sup:1mmzj4cu] - 2x| + |1|, finding the maximum value of each on the interval from x = -2 to x = 3 and summing to find the results.

What did you get when you tried each combination?

Please be specific. Thank you! :D

Eliz.
 
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