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anonymous
 3 years ago
Find an equation of the tangent line to y = f(x) at x = 1. f(x) 3e^x
anonymous
 3 years ago
Find an equation of the tangent line to y = f(x) at x = 1. f(x) 3e^x

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anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0@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?

zepdrix
 3 years ago
Best ResponseYou've already chosen the best response.1sup? c: what part confusing you?

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0okay 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
 3 years ago
Best ResponseYou've already chosen the best response.1Yah it's a weird looking number, so I can see how it's a little confusing. So you calculated the slope, \(\large m\). \(\large m=3e \qquad \rightarrow \qquad y=(3e)x+b\)

zepdrix
 3 years ago
Best ResponseYou've already chosen the best response.1To 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
 3 years ago
Best ResponseYou've already chosen the best response.0hmmm 1 in the original question that would be our x and for y we would put 1 into 3e^x

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0okay so our coordiantes will be (1, 3e) ? since when you plug in 1 into 3e^1 you get 3e

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0wait i meant 1 = 3e(1) + b

zepdrix
 3 years ago
Best ResponseYou've already chosen the best response.1\[\huge \left(\color{orangered}{x},\;\color{royalblue}{y}\right) \qquad = \qquad \left(\color{orangered}{1},\;\color{royalblue}{3e}\right)\]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
 3 years ago
Best ResponseYou've already chosen the best response.0okay then i solve for be and i'm done right?

zepdrix
 3 years ago
Best ResponseYou've already chosen the best response.1Yes, solve for b. Then rewrite your final equatoin with y, x, m and b. Good job c:

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0so i fot 3e = 3e(1) + 0

zepdrix
 3 years ago
Best ResponseYou've already chosen the best response.1yes, 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
 3 years ago
Best ResponseYou've already chosen the best response.0ok how would i do that?

zepdrix
 3 years ago
Best ResponseYou've already chosen the best response.1Remember 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.
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