onegirl Group Title Find an equation of the tangent line to y = f(x) at x = 1. f(x) 3e^x one year ago one year ago

1. onegirl Group Title

@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 Group Title

@Mertsj can u help?

3. zepdrix Group Title

sup? c: what part confusing you?

4. onegirl Group Title

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 Group Title

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 Group Title

okay

7. zepdrix Group Title

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 Group Title

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

9. zepdrix Group Title

k sounds good.

10. onegirl Group Title

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

11. zepdrix Group Title

yes.

12. onegirl Group Title

okay

13. onegirl Group Title

so 1 = (3e)x + b ?

14. onegirl Group Title

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

15. zepdrix Group Title

$\huge \left(\color{orangered}{x},\;\color{royalblue}{y}\right) \qquad = \qquad \left(\color{orangered}{1},\;\color{royalblue}{3e}\right)$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 Group Title

ohhh okay hold on

17. onegirl Group Title

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

18. zepdrix Group Title

yes.

19. onegirl Group Title

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

20. zepdrix Group Title

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

21. onegirl Group Title

okay

22. onegirl Group Title

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

23. zepdrix Group Title

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 Group Title

ok how would i do that?

25. zepdrix Group Title

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 Group Title

x=x y=y :d

27. onegirl Group Title

ok