Question

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

Answer 1

@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?

Answer 2

@Mertsj can u help?

Answer 3

sup? c: what part confusing you?

Answer 4

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

Answer 5

Yah it's a weird looking number, so I can see how it's a little confusing.
So you calculated the slope, \(\large m\).

\(\large m=3e \qquad \rightarrow \qquad y=(3e)x+b\)

Answer 6

okay

Answer 7

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

Answer 8

hmmm 1 in the original question that would be our x and for y we would put 1 into 3e^x

Answer 9

k sounds good.

Answer 10

okay so our coordiantes will be (1, 3e) ? since when you plug in 1 into 3e^1 you get 3e

Answer 11

yes.

Answer 12

okay

Answer 13

so 1 = (3e)x + b ?

Answer 14

wait i meant 1 = 3e(1) + b

Answer 15

\[\huge \left(\color{orangered}{x},\;\color{royalblue}{y}\right) \qquad = \qquad \left(\color{orangered}{1},\;\color{royalblue}{3e}\right)\]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.

Answer 16

ohhh okay hold on

Answer 17

so 3e = 3e(1) + b?

Answer 18

yes.

Answer 19

okay then i solve for be and i'm done right?

Answer 20

Yes, solve for b. Then rewrite your final equatoin with y, x, m and b.
Good job c:

Answer 21

okay

Answer 22

so i fot 3e = 3e(1) + 0

Answer 23

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.

Answer 24

ok how would i do that?

Answer 25

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.

Answer 26

x=x
y=y

:d

Answer 27

ok