Derivatives: Composites, normal lines, nth derivatives and more.by StopWatch Tags: composites, derivatives, lines, normal 

#1
Jun2211, 03:23 PM

P: 38

1. The problem statement, all variables and given/known data
1. The line perpendicular to the curve y = 2x^3  x^2 + x  3 at the point (1, 1) will intersect the xaxis at what point? 2. f(x) = x^2  5  x, for all x. Let g = f(f(f(x))), find g'(2). I tried just subbing in 2x  1, the first derivative, to f(2x  1) and then once more and ended up with 16 somehow, when the answer is 45. 3. If f(x) = ln(2X^2 + x  1)  ln(x+1) find the 98th derivative at (1/2 + sqrt(2)/2). I know that the derivative simplifies to 2(2x  1) and the 2nd derivative to 2/(2x1)^2 and the 3rd to 8(2x1)/2x1)^4 but I always have a hard time generalizing these and then getting the answer (especially because the answer is 2^49(97!) and I have no idea how the factorial gets worked in. 2. Relevant equations y1  y0 = m(x1  x0) 3. The attempt at a solution Finding the derivative and subbing in x = 1 gives a slope of 5 at the point specified, which means m = 1/5. When solved this gives x = 10, however the correct answer is apparently 4. This site is a godsend. 



#2
Jun2211, 05:00 PM

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Hi StopWatch!




#3
Jun2211, 05:09 PM

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#4
Jun2211, 09:22 PM

P: 38

Derivatives: Composites, normal lines, nth derivatives and more.
Is the nth derivative (n!)x^n? Does that make sense. Sorry for leaving for so long I had class. I hope someone's around though, the test is tomorrow morning and I have a ton of questions. I wish professors posted solutions to past tests. I redid the algebra and got 10 by the way y (which is zero when the x axis is intercepted) + 1 = 5(x  1), so 0 = 5x 2 = 2/5 somehow I really screwed that up, wow.
It can be negative, but we're subbing in when x = 2 so those cases don't matter, or at least that's my logic. My main concern is about how to actually go about plugging into the composite like that. I do have a new question as well though: The line perpendicular to x^3  2x + 1 at (2, 5) will intersect the xaxis at what point? I get (y5) = 10(x2) which gives me 15/10 for the x value of the tangent. I might just be really rushed in my thinking right now I'd really appreciate any help at all. 



#5
Jun2211, 09:53 PM

P: 38

Anyone around?




#6
Jun2311, 04:17 AM

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Hi StopWatch!
(just got up …) but anyway it's (x  1) = 5(1) Anyway, good luck on your test this morning! 


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