anonymous
  • anonymous
Find an equation of the tangent line to y = f(x) at x = 1. f(x) 3e^x
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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chestercat
  • chestercat
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anonymous
  • anonymous
@zepdrix hi can u help for a minute i know how to do this since you showed me yesterday how..but i'm stuck on something, so can u help?
anonymous
  • anonymous
@Mertsj can u help?
zepdrix
  • zepdrix
sup? c: what part confusing you?

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anonymous
  • anonymous
okay so i tried doing this one here is what i got so far i found the derivative of 3e^x and i got d/dx (3e^x) = 3(d/dx (e^x)) = 3e^x so now I filled in the 1 into 3e^x and I got 3e so i want to put it into y=mx + b and i got stuck there
zepdrix
  • zepdrix
Yah it's a weird looking number, so I can see how it's a little confusing. So you calculated the slope, \(\large m\). \(\large m=3e \qquad \rightarrow \qquad y=(3e)x+b\)
anonymous
  • anonymous
okay
zepdrix
  • zepdrix
To solve for \(\large b\) remember that we needed a coordinate pair that we could plug into this. Where can we get a coordinate pair from? :o
anonymous
  • anonymous
hmmm 1 in the original question that would be our x and for y we would put 1 into 3e^x
zepdrix
  • zepdrix
k sounds good.
anonymous
  • anonymous
okay so our coordiantes will be (1, 3e) ? since when you plug in 1 into 3e^1 you get 3e
zepdrix
  • zepdrix
yes.
anonymous
  • anonymous
okay
anonymous
  • anonymous
so 1 = (3e)x + b ?
anonymous
  • anonymous
wait i meant 1 = 3e(1) + b
zepdrix
  • zepdrix
\[\huge \left(\color{orangered}{x},\;\color{royalblue}{y}\right) \qquad = \qquad \left(\color{orangered}{1},\;\color{royalblue}{3e}\right)\]Plug those into here,\[\huge \color{royalblue}{y}=(3e)\color{orangered}{x}+b\] You didn't quite get them plugged in correctly. Maybe the colors will help you match them up.
anonymous
  • anonymous
ohhh okay hold on
anonymous
  • anonymous
so 3e = 3e(1) + b?
zepdrix
  • zepdrix
yes.
anonymous
  • anonymous
okay then i solve for be and i'm done right?
zepdrix
  • zepdrix
Yes, solve for b. Then rewrite your final equatoin with y, x, m and b. Good job c:
anonymous
  • anonymous
okay
anonymous
  • anonymous
so i fot 3e = 3e(1) + 0
zepdrix
  • zepdrix
yes, but you want to write it as an equation involving x and y. We no longer want the coordinate pair plugged in for our final answer.
anonymous
  • anonymous
ok how would i do that?
zepdrix
  • zepdrix
Remember we were trying to come up with an equation for the tangent line. It will be of the form \(\large y=mx+b\). We ONLY want to fill in the missing \(\large m\) and \(\large b\). We had plugged in our coordinate pair to help us find \(\large b\), but now we don't need that coordinate pair.
zepdrix
  • zepdrix
x=x y=y :d
anonymous
  • anonymous
ok

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