anonymous
  • anonymous
how did 3x+2y-7=0 became the equation of the tangent line if the given is f(x)= 2/fourthroot(x^3) and P(1,2) please explain it to me :(
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
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DebbieG
  • DebbieG
\[\Large f(x)=\frac{ 2 }{ \sqrt[4]{x^3} }= 2x^{-3/4}\] \[\Large f\prime(x)= -\frac{ 3 }{ 2 } x^{-7/4}\] Did you get that much so far?
DebbieG
  • DebbieG
If so, then evaluate \(\Large f\prime(1)\). That gives you the slope of the tangent line. You are given a point on the line. Plug the slope and point into whatever form of line equation suits your fancy (I used point-slope) and solve so that you have the form Ax + By + C=0 You should get the line given. :)
anonymous
  • anonymous
i got the first one.. how did the second one became -3/2? i do understand the happening in the exponent though.. im sorry im not good in math :(

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DebbieG
  • DebbieG
Do you know how to take a derivative? (I'm assuming so, in light of this question.)
anonymous
  • anonymous
yes i do, but i'm not really good at it.. i can get derivatives of simple equations, but when the given becomes complicated, i am lost of finding its derivative :(
DebbieG
  • DebbieG
\[\Large \left[ Cx^n \right]\prime=Cnx^{n-1}\]
DebbieG
  • DebbieG
Ok, NO NEED FOR SAD FACE. :) Math is happy. We'll just go through it.... hang on....
DebbieG
  • DebbieG
\(\Large f(x)= 2x^{-3/4}\) \(\Large f\prime(x)= 2\cdot \dfrac{-3}{4} x^{-3/4-1}\)
DebbieG
  • DebbieG
\[\Large \cancel2\cdot \dfrac{-3}{\cancel4^2} x^{-3/4-4/4}\]
anonymous
  • anonymous
got that :)
DebbieG
  • DebbieG
\(=\Large \dfrac{-3}{2} x^{-7/4}\)
DebbieG
  • DebbieG
K? Good on that? That's your derivative. :)
anonymous
  • anonymous
yes.. thank you so much :) big big help for me.. :) :) :) :) :)
DebbieG
  • DebbieG
I did it prettier the first time.... lol \(\Large f\prime(x)= -\frac{ 3 }{ 2 } x^{-7/4}\)
DebbieG
  • DebbieG
Great! You ok from here?
anonymous
  • anonymous
i hope so! i'm currently trying to solve it.. :) but thank you, youre a big help. i understood it now :)
DebbieG
  • DebbieG
Happy to help! :)
anonymous
  • anonymous
3x+2y-7=0 first solve for y you'd get y=(-3 /2)x+7/2 --- Maybe you dont have to but to me it is easier with y=mx+b form 2/(x^3) ^(1/4) BTW ^(1/4) is like saying 4th rooth I wanna try it graphically https://www.google.com/search?q=(-3+%2F2)x%2B7%2F2%2C+2%2F(x%5E3)+%5E(1%2F4)&oq=(-3+%2F2)x%2B7%2F2%2C+2%2F(x%5E3)+%5E(1%2F4)&aqs=chrome..69i57.5801j0&sourceid=chrome&ie=UTF-8 As you can see it is a tangent :)
anonymous
  • anonymous
wow, thank you for that :) i'm a fan :)))) got it! thanks for the graph, big help @timo86m :)
DebbieG
  • DebbieG
Here is another cool graphing tool.... I like that you can put the equation in as-is, don't have to solve for y. :) It's always fun to "see" the math!! It doesn't help you DO the problem, but it does help you see the connection visually, and have confidence that the answer is right http://kevinmehall.net/p/equationexplorer/#3x+2y-7=0|2/%28x^%283/4%29%29|[-10,10,-10,10]
anonymous
  • anonymous
algebraically tho i think you would need to solve a system of equations 2/(x^3) ^(1/4)=y (-3 /2)x+7/2 = y which is (-3 /2)x+7/2= 2/(x^3) ^(1/4) I think that is how it is done. the solution should be P(1,2)
DebbieG
  • DebbieG
ugh, you'll have to c&p that broken link.
anonymous
  • anonymous
http://www.wolframalpha.com/ works too :) input more than 1 equation or expressions with a ,
anonymous
  • anonymous
algebraically tho i think you would need to solve a system of equations 2/(x^3) ^(1/4)=y 1 2 (-3 /2)x+7/2 = y which is 1 2 (-3 /2)x+7/2= 2/(x^3) ^(1/4) I think that is how it is done. the solution should be P(1,2) ---p 1,2
anonymous
  • anonymous
thank you to both of you, i really appreciate it :)
anonymous
  • anonymous
Also dont forget f'(x) gives you the slope at x. It doesn't give you an equation to draw it for you. y=mx+b draws a line for you. But f'(x) only gives you the m part of it. so lets say f'(3)=2 then you know the slope aka m at c=2 y=2*3+b plug the known info to y=mx+b: m and x y is gotten thru f(3)= y lets say it is 4 f(3)= 4 4=2*3+b now you simply solve for b cuzz you got enough info for it. b=-2 now you can you plug x and y back to the traditional y=mx+b y=2x-2
anonymous
  • anonymous
thank you so much @timo86m wow, math wizard :)
anonymous
  • anonymous
|dw:1377720764480:dw| this will be how it looks graphicaly
anonymous
  • anonymous
that is just the tangent line but f(x) could look like many things |dw:1377720897260:dw| |dw:1377720911029:dw| |dw:1377720925245:dw| Anything really so long as it is a tangent at 3,4
anonymous
  • anonymous
I noticed i didn't do this |dw:1377721330155:dw| that might confuse some but that is still a tangent line at 3,4 even tho it touched 2 places. Usually we only concern ourselves at the interval of 3,4 in this problem.

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