May 25th, 2012, 03:31 PM  #1 
Member Joined: Jan 2012 Posts: 43 Thanks: 0  Tangent line equation
Hey, I'm having trouble with a quotient rule problem that asks you to find the equation of the tangent line. The function is The question then states that when x=9 the corresponding y value will be______ and the slope of the tangent line Is f'(x)=9=_______. Thererore the equation of the tangent line is_______? In form ax+b. For the first blank I just inserted x=9 into the original equation and solved f(x)=53. For the second blank I got the slope equalling 55/9 by plugging x=9 into the derivative of f(x). I Calculated the Derivative using the product rule And ended up with a derivative of: For the tangent line equation I got By plugging in the coordinates (9,53) to y+53=(55/9)x9 Some part here is incorrect I am not sure which, any help would be much appreciated 
May 25th, 2012, 03:39 PM  #2 
Senior Member Joined: May 2011 Posts: 501 Thanks: 6  Re: Tangent line equation
If you plug x=9 into the derivative , you should get . Also, , as you correctly have. So, you now have x=9, y=53, m=163/18. All set to find line equation. It may be a little easier to find the derivative by expanding f(x) into Then, termbyterm, we get . Or you can write it as I have above. Just another equivalent form. Is that a picture of you with a TI?. Good to see you're into math. Count yourself as a member of a small minority of the overall population. 
May 25th, 2012, 03:59 PM  #3 
Global Moderator Joined: Oct 2008 From: London, Ontario, Canada  The Forest City Posts: 7,963 Thanks: 1148 Math Focus: Elementary mathematics and beyond  Re: Tangent line equation
Though galactus mentioned it (while I was posting ), here is another approach: Now it is a little easier to differentiate. 
May 25th, 2012, 10:32 PM  #4 
Member Joined: Jan 2012 Posts: 43 Thanks: 0  Re: Tangent line equation
Ya thanks guys I haven't dealt with product quotient rules in awhile so the different approaches are very helpful as i get back into things. And ya galactus I've always enjoyed math, although the program I'm in is calling for less and less of it as I near the end, unfortunately..


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