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 November 1st, 2011, 12:50 PM #1 Newbie   Joined: Nov 2011 Posts: 2 Thanks: 0 First Deriv test, finding critical numbers of this.Need help So I don't have class for another week and I have a question about this problem. I understand the steps in order to do this, it's just the power that messes me up while doing the algebra parts of these calc problems. 1. Find all the x-intercepts of the function f(x)= X^5 - X. Express as ordered pairs. *The 5th power messes me up here. Can anyone walk me through how to properly do this while dealing with that 5th? 2. The y-intercept occurs at the point ____. *I just plug the x problem into the original function to get this right? 3. The first deriv of the function: This I got to be 5X^4 - 1 4. Set the first deriv equal to zero, find the critical values of the function. Round to the thousandths place when necessary. *I've tried this a couple different ways but I keep messing up with the 4th power up there.. I can't seem to get it right. I'm fine on the easier problems but when the powers get higher I get messed up on it. The rest is just finding increasing/decreasing, max/mins, etc. I know how to do those.. I just have trouble finding the x-interceps in #1 and finding the critical values in #4. Can anyone help me with this? Those powers keep messing me up.. Thanks
November 1st, 2011, 01:50 PM   #2
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Re: First Deriv test, finding critical numbers of this.Need

Quote:
 Originally Posted by steelcurtain11 1. Find all the x-intercepts of the function f(x)= X^5 - X. Express as ordered pairs.
Factor:

$x^5\,-\,x\,=\,x(x^4\,-\,1)\,=\,x(x^2\,-\,1)(x^2\,+\,1)$

The x-intercepts are where the function = 0:

$x(x^2\,-\,1)(x^2\,+\,1)\,=\,0\,\Rightarrow\,x\,=\,0,\,x^2\ ,-\,1\,=\,0,\,x^2\,+\,1\,=\,0\,\Rightarrow\,(-1,\,0),\,(0,\,0),\,(1,\,0)\text{ are the three }x{\text{-intercepts.}$

$x^2\,+\,1\,=\,0\text{ has no real roots.}$

2. The y-intercept occurs at the point x = 0, for any function. For this function it is at (0, 0).

3. Correct.

4.

$5x^4\,-\,1\,=\,0$

$x^4\,=\,\frac{1}{5}$

$x\,=\,\pm\,\frac{1}{5^{\small{1/4}}}$

 November 1st, 2011, 06:51 PM #3 Newbie   Joined: Nov 2011 Posts: 2 Thanks: 0 Re: First Deriv test, finding critical numbers of this.Need Thank you! This helped me a lot. I had something close to that, it really helped me figure out how to deal with the algebra better.

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