SOLUTION: x^2-3x^5>10

Question 821307: x^2-3x^5>10
Answer by KMST(5328) (Show Source): You can put this solution on YOUR website!

A graphing calculator would tell you that
happens for (rounded),
with the only for .
Before graphing calculators, I would have calculated the derivative as
=
Since the last factor is always positive, the zeros of the derivative are at and at .
The derivative is negative in between those two values of ,
meaning that is an interval where decreases.
For other values of , the derivative is positive and the function increases.
At where we have a maximum of ,
and at , a minimum of , where .
Since and ,
The value of that makes is in between, .
At that point we would try guess-and-check values in between, aiming to get closer limits on , maybe going through
, , and so on, until I got a close enough approximation.
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