## onegirl 2 years ago Find an equation of the tangent line to y = f(x) at x = 1. f(x) 3e^x

1. onegirl

@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?

2. onegirl

@Mertsj can u help?

3. zepdrix

sup? c: what part confusing you?

4. onegirl

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

5. zepdrix

Yah it's a weird looking number, so I can see how it's a little confusing. So you calculated the slope, $$\large m$$. $$\large m=3e \qquad \rightarrow \qquad y=(3e)x+b$$

6. onegirl

okay

7. 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

8. onegirl

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

9. zepdrix

k sounds good.

10. onegirl

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

11. zepdrix

yes.

12. onegirl

okay

13. onegirl

so 1 = (3e)x + b ?

14. onegirl

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

15. 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.

16. onegirl

ohhh okay hold on

17. onegirl

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

18. zepdrix

yes.

19. onegirl

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

20. zepdrix

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

21. onegirl

okay

22. onegirl

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

23. 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.

24. onegirl

ok how would i do that?

25. 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.

26. zepdrix

x=x y=y :d

27. onegirl

ok