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Let $$f(x)={x^3-14x^2+7x+203\over(x-3)(8-x)}$$ I want to find the two solutions of $$f(x)f''(x)=(f'(x))^2,\qquad3\le x\le8$$

This is the first time i am using maple, and i cannot get the graph to work out.

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Which functions "intersect"? Which graph are you wanting to work out? –  Gerry Myerson Apr 26 '12 at 13:33
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Reading your post is a nightmare. Could you please write mathematics in some less "computer science" fashion? –  Siminore Apr 26 '12 at 13:33
    
edited, i removed the first and second Der. to make the post cleaner. I believe you all should be able to calculate these, so its not important for me question. –  Special--k Apr 26 '12 at 13:44
    
@Siminore better? –  Special--k Apr 26 '12 at 15:26
    
What are the functions you are trying to find the intersection of????? –  000 Apr 26 '12 at 15:45
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2 Answers

up vote 2 down vote accepted

Using Maple 16 ...

computation

Note $F1 > -10$ and $F2 > 50$, so there is no need to consider the absolute value of $F1$ for intersections.

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The first derivative is $3 x^2-28 x+ \frac {203}{5 (x-8)^2}-\frac {203}{5 (x-3)^2}+7$ and the second is $\frac {14}5 \left(\frac{29}{(x-3)^3}-\frac{29}{(x-8)^3}-10\right )+6 x$ (both from Alpha). Unfortunately, the entry box isn't large enough for your whole problem, but a lot of the denominators will cancel.

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