## cpt one year ago If f(x) is continuous and differentiable and f(x) = ... then b? f(x) = {ax^4 + 5x, x< or = 2 {bx^2 - 3x, x> 2, then b = ? Help pls

1. myininaya

1st set these two expressions equal to each other: $\lim_{x \rightarrow 2^-}f(x)=\lim_{x \rightarrow 2^+}f(x)$

2. myininaya

2nd set these two expressions equal to each other: $\lim_{x \rightarrow 2^-}f'(x)=\lim_{x \rightarrow 2^+}f'(x)$

3. cpt

What should I do after that? Add those two equations together?

4. myininaya

You will have a system of equations to solve just like from algebra class.

5. cpt

Well I got, 4a - 10 = 4b - 6 and then -32 + 5 = 4b - 3. Is that correct?

6. myininaya

The first equation on the left hand side you have 4a-10 I think it should be 16a+10. What happen to a in the second expression?

7. myininaya

I mean equation err

8. cpt

oops you are right.

9. myininaya

$a(2)^4+5(2)=b(2)^2-3(2) \text{ first equation }$

10. myininaya

$4a(2)^3+5=2b(2)-3 \text{ second equation }$

11. cpt

Wait isn't it a(-2)^4 + 5 (-2) since the limit is coming from the left side?

12. myininaya

It isn't approaching -2. It is approaching 2.

13. myininaya

You have the left is just approaching 2 from the left. You have the right is just approaching 2 from the right. Either way they are both still approaching 2 and not some other number.

14. cpt

Ahh ok I got it :) After I get these 2 equations then what should I do afterward?

15. myininaya

Have you ever solved a system of two linear equations?

16. cpt

Yes, like 4 years ago haha.

17. cpt

16a + 10 4b - 6 32a + 5 4b - 3 ( Can't I just substitute it and then solve it) ?

18. myininaya

You can put them both in ax+by=c form if you want. Like if we had something like 2x+3y=1 -2x+3y=1 This system is already set up for elimination. Add the equations together and solve for y first would be my strategy. 6y=2 y=2/6=1/3 Then plug into one of the other equations and solve for x.

19. myininaya

Or this system: 3x-6y=2 x+y=2 This one isn't set up for elimination. But you could multiply the bottom equation by -3 so we would have it setup for elmination. 3x-6y=2 -3x-3y=-6 ----------------add -9y=-4 y=4/9 and then so on to find x.

20. myininaya

$a(2)^4+5(2)=b(2)^2-3(2) \text{ first equation }$ $16a+10=4b-6$ $16a-4b=-16 \text{ rewrote the equation 1}$

21. myininaya

Do you think you can rewrite equation 2 in that form?

22. cpt

32a - 4b = -8 ( 2nd equation right) right?

23. myininaya

looks good

24. myininaya

So we have 16a-4b=-16 32a-4b=-8

25. myininaya

If we multiply the second or even the first (just not both of them) by -1, then we can set this up for elimination method.

26. myininaya

I'm trying to eliminate b. (you could go for a but I prefer working with smaller numbers)

27. myininaya

So -16a+4b=16 32a-4b=-8 ----------------add the equations together and what do we get?

28. cpt

I got the final answer of 6 for b. Is that right?

29. cpt

and .5 for a

30. myininaya

yep. good job.

31. cpt

yayyy, you should just be my tutor haha. Thank you so much :D

32. myininaya

np