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Determine an equation of the line tangent to the graph of
y= ((x^21)^2)/(x^36x1) at the point (3,8)
 6 months ago
 6 months ago
Determine an equation of the line tangent to the graph of y= ((x^21)^2)/(x^36x1) at the point (3,8)
 6 months ago
 6 months ago

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myininayaBest ResponseYou've already chosen the best response.1
\[y=\frac{(x^21)^2}{x^36x1}\] Have you found y' yet?
 6 months ago

natka107Best ResponseYou've already chosen the best response.0
Yes, I have but I am getting the final answer wrong, and I am not sure where I am making a mistake. It is the first time I can't figure out what I am doing wrong...
 6 months ago

myininayaBest ResponseYou've already chosen the best response.1
So you have \[((x^21)^2)'=2(x^21) \cdot 2x \] and \[(x^36x1)'=3x^26\] ?
 6 months ago

myininayaBest ResponseYou've already chosen the best response.1
So by quotient rule, we should have \[y'=\frac{2(x^21) \cdot 2x (x^36x1)(3x^26)(x^21)^2}{(x^36x1)^2}\]
 6 months ago

myininayaBest ResponseYou've already chosen the best response.1
What did you get for the slope? I got a pretty little integer.
 6 months ago

myininayaBest ResponseYou've already chosen the best response.1
Say something so I can know you are still there. Like did you simplify that above and then plug in? I'm getting the slope of the tangent at x=3 is 9.
 6 months ago

natka107Best ResponseYou've already chosen the best response.0
sorry. The answer is y=9x+35
 6 months ago

natka107Best ResponseYou've already chosen the best response.0
I got some bizzare answers that don't make much sense... However, for y' i got \[((x^21)(x^415x^24x6))\div(x^36x1)^2\]
 6 months ago

natka107Best ResponseYou've already chosen the best response.0
myininaya how did you get 9 and 3?
 6 months ago

myininayaBest ResponseYou've already chosen the best response.1
Your question said to find the tangent line at x=3. I plugged x=3 into f'.
 6 months ago

natka107Best ResponseYou've already chosen the best response.0
I did that and still did something wrong. Anyways, thanks for your help.
 6 months ago

myininayaBest ResponseYou've already chosen the best response.1
You y' is right... I don't understand why you aren't getting 9 when pluggin in 3.... \[\frac{(3^21)(3^415(3)^24(3)6)}{(3^36(3)1)^2}\] \[=\frac{(91)(81135126)}{(27181)^2}=\frac{(8)(81153)}{(2719)^2}\] \[=\frac{(8)(72)}{(8)^2}=\frac{8(72)}{(8)(8)}=\frac{\cancel{8}(72)}{\cancel{(8)}(8)}=\frac{72}{8}=9\]
 6 months ago

myininayaBest ResponseYou've already chosen the best response.1
You should be getting 9 as the slope of your line... So I don't know where you are going wrong in your calculation.
 6 months ago

natka107Best ResponseYou've already chosen the best response.0
Hah, I found my mistake! I kept calculating 3^2 instead of 3^3 in the denominator...
 6 months ago
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