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eroshea
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find the equation of the tangent and normal line to the curve y=2x^3  3x^2 2x +5, where x =1
 one year ago
 one year ago
eroshea Group Title
find the equation of the tangent and normal line to the curve y=2x^3  3x^2 2x +5, where x =1
 one year ago
 one year ago

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terenzreignz Group TitleBest ResponseYou've already chosen the best response.2
To get a line, you need a slope, and a point, right? Or, knowing the slope of a line and a point where it passes through, that's sufficient to find the equation of the line, yes?
 one year ago

eroshea Group TitleBest ResponseYou've already chosen the best response.1
yes.. so how will i find the slope?
 one year ago

terenzreignz Group TitleBest ResponseYou've already chosen the best response.2
Magic. Or, you can differentiate this function first... go ahead now :) Remember, the slope of the tangent line at the point would be its derivative, while the slope of the normal line would be the negative reciprocal of the derivative.
 one year ago

terenzreignz Group TitleBest ResponseYou've already chosen the best response.2
Start by differentiating, though.
 one year ago

eroshea Group TitleBest ResponseYou've already chosen the best response.1
dy/dx = 6x^2  6x 2
 one year ago

terenzreignz Group TitleBest ResponseYou've already chosen the best response.2
Quick to the point, are we? :) Now, when x = 1, what's dy/dx?
 one year ago

eroshea Group TitleBest ResponseYou've already chosen the best response.1
dy/dx = 2
 one year ago

terenzreignz Group TitleBest ResponseYou've already chosen the best response.2
And that is the slope of your tangent line :) What's the slope of your normal line? (Remember, the normal line is *perpendicular* to the tangent line)
 one year ago

eroshea Group TitleBest ResponseYou've already chosen the best response.1
negative reciprocal of it.. 1/2
 one year ago

terenzreignz Group TitleBest ResponseYou've already chosen the best response.2
And that is the slope of the normal line. So you have the slopes for both lines, you now only need a point. Any idea how to get one?
 one year ago

eroshea Group TitleBest ResponseYou've already chosen the best response.1
hmm.. where they would intersect? but i don't know how
 one year ago

terenzreignz Group TitleBest ResponseYou've already chosen the best response.2
Well, both the tangent and the normal would intersect your curve at the point WHERE x = 1. So at the curve itself, when x = 1, what is y? :P
 one year ago

eroshea Group TitleBest ResponseYou've already chosen the best response.1
then i just need to use slope intercept form , right? with P(1,2) and a slope of 1/2?
 one year ago

terenzreignz Group TitleBest ResponseYou've already chosen the best response.2
No... that's dy/dx I meant y. You know... your original curve? :P
 one year ago

terenzreignz Group TitleBest ResponseYou've already chosen the best response.2
y=2x^3  3x^2 2x +5
 one year ago

eroshea Group TitleBest ResponseYou've already chosen the best response.1
y = 8.. sorry
 one year ago

eroshea Group TitleBest ResponseYou've already chosen the best response.1
wrong again!
 one year ago

terenzreignz Group TitleBest ResponseYou've already chosen the best response.2
LOL don't worry about that :) So you have a point (1 , 8) and you have a slope (2 for your tangent, 1/2 for your normal) You can't use a slope intercept form, you need the more general pointslope form. When you have a point \(\large (\color{red}p,\color{green}q)\) and a slope \(\large \color{blue}m\) then the equation of the line is: \[\Large y = \color{blue}m(x\color{red}p)+\color{green}q\]
 one year ago

eroshea Group TitleBest ResponseYou've already chosen the best response.1
OWH.. i got 2 again
 one year ago

eroshea Group TitleBest ResponseYou've already chosen the best response.1
its 2 right?
 one year ago

terenzreignz Group TitleBest ResponseYou've already chosen the best response.2
What is? Your slope? No, you were right, it's 2 for the tangent.
 one year ago

eroshea Group TitleBest ResponseYou've already chosen the best response.1
no .. the coordinates of the point (1,2)
 one year ago

terenzreignz Group TitleBest ResponseYou've already chosen the best response.2
Ah well then, it won't be (1,8) but (1,2) instead :) Work with that then. :D
 one year ago

terenzreignz Group TitleBest ResponseYou've already chosen the best response.2
\[\Large y = \color{blue}m(x\color{red}p)+\color{green}q\]
 one year ago

eroshea Group TitleBest ResponseYou've already chosen the best response.1
y = 2x + 4 ?
 one year ago

terenzreignz Group TitleBest ResponseYou've already chosen the best response.2
correct :) Now the normal line? the only difference is the slope :)
 one year ago

terenzreignz Group TitleBest ResponseYou've already chosen the best response.2
and you're done :P
 one year ago

eroshea Group TitleBest ResponseYou've already chosen the best response.1
:D thanks kiddo .. but you're smarter than me
 one year ago

terenzreignz Group TitleBest ResponseYou've already chosen the best response.2
Nah. I've just read in advance :P
 one year ago
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