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Homework Statement
Given
Homework Equations
The Attempt at a Solution
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I know I found that it is increasing on the interval (-1,1), but that's wrongIf I remember correctly, f(x) is an increasing function for f'(x) > 0 and a decreasing function for f'(x)< 0.
ok I re-did it again because I found an errorHow did you get that?
it's a straight light, and on the original function that means that there's a point there where it is neither increasing or decreasing or a max or min.Now how about d and e?
Here's a clue...
What is the shape of the graph when the derivative is zero?
in the numerator: -1,1Hmm...
I'm sorry, but I don't get (-1,3) for increasing...
The derivative is this, as you have written, correct?
[tex]\frac{5(1-x)(x-1)}{(3x^2-10x+3)^2}[/tex]
Ignore the denominator... where is the numerator zero? Where are each of the three components zero?
That's what I did when I first started it and I got (-1,1) as increasing but that's wrong.....I said ignore the denominator... if the denominator is zero, your graph is really screwing up.
OK, so you know the graph of the derivative is zero at -1 and 1.
Thus, the minimum and the maximum must be at those two points.
there's an error at 3 too, so does that mean I do count the denominator?There's a singularity at x=1/3, which is in (-1,1). That's probably why.
huh?Oh...
So it would be -1<x<1, x=/=(1/3) then...
ok, so I redid it over again and do you think these are correct:Yes, exactly. The function isn't increasing at x=1/3 because it isn't defined there, so you have to split the interval as you have done.
nothing important, that was a typo, how about this for an answer:What happens between x=-2 and x=-1?