<p>If, -1 < x < 0, which of the following statement must be true?</p>
<p>(A) x < x^2 < x^3
(B) x < x^3 < x^2
(C) x^2 < x < x^3
(D) x^2 < x^3 < x
(E) x^3 < x < x^2</p>
<p>Use a calculator to produce values (don't have one in front of me).</p>
<p>Use -.05 as X (well you could utilize other numbers, but get a number in the given range).</p>
<p>I did, and it doesn't work</p>
<p>the answer is A</p>
<p>the answer is not A
the answer is B</p>
<p>use the value -.5</p>
<p>B) -.5< -.125< .25</p>
<p>If -1 < x < 0, then 0 < x^2 < 1 and -1 < x^3 < 0 . Note that x^2 is a positive number; both x and x^3 are negative numbers.</p>
<p>You can use this to eliminate several of the choices:
(A) x < x^2 < x^3 No, because x^2 cannot be < x^3 (for -1 < x < 0)
(B) x < x^3 < x^2 Maybe
(C) x^2 < x < x^3 No, because x^2 cannot be < x ( for ...)
(D) x^2 < x^3 < x No, same reason
(E) x^3 < x < x^2 Maybe</p>
<p>The answer is either (B) or (E). You can plug in a couple of sample x values like -0.1 and -0.5 (as chances_please16 did) to verify that (B) is correct.</p>
<p>(If your geometry and visualization capabilities are good :), you can visualize the curves for f(x) = x and g(x) = x^3 and see how they behave when -1 < x < 0 )</p>
<p><a href="If%20your%20geometry%20and%20visualization%20capabilities%20are%20good%20,%20you%20can%20visualize%20the%20curves%20for%20f(x)%20=%20x%20and%20g(x)%20=%20x%5E3%20and%20see%20how%20they%20behave%20when%20-1%20%3C%20x%20%3C%200">quote</a>
[/quote]
wow, you could do that optimizerdad?</p>
<p>^lol its not that hard :d</p>
<p>whoops, i went from greatest to least, thats probably why I only got a 700 on the math section</p>