## iop360 3 years ago determine the values of constant real numbers a and b, so that this function is differentiable at x= -5 f(x) = (ax^2) - 4x -76 x<=(-5) = bx - 1 x > 5

1. iop360

\[ax^2 - 4x - 76, x \le -5\] \[bx -1, x > -5\]

2. iop360

answers are a = -3 b = 26

3. iop360

what do i do to get the answers though

4. zepdrix

Hmm are you sure it's -76? Or is it suppose to be 75? I get a=-3 if its a 75.. hmm Sec ill check my work, then I can hopefully explain how i got there.

5. iop360

yes it is -76

6. zepdrix

|dw:1349558391356:dw| Here is a little example. In order for this piece-wise function be continuous, the limit from the left, needs to EQUAL, the limit from the right (approaching -5). That's why I drew those little arrows, to show that we're approaching -5 from each side. Also, their tangent line's need to be approaching the same value at that point -5. Meaning, their derivatives must be equal when approaching from the left and right. So we have a little bit of work to do. And it will give us a system of 2 equations, and we'll be able to solve for a and b from there.

7. iop360

oh ok

8. iop360

do we differentiate each equation

9. zepdrix

|dw:1349558662733:dw|

10. zepdrix

Oh i see where I made a mistake in my notes :) ok ok good this will work out fine I think.

11. zepdrix

|dw:1349558827441:dw| the -20 should be a +20 in the first picture i did.

12. zepdrix

|dw:1349558961847:dw| And from here, you have a system of equations and should be able to solve for a and b!! :) If you're stuck on how to solve the system, you can let me know.

13. iop360

so we have a choice of what equations wewant to use to solve for a and b?

14. zepdrix

Mmmm no i think we have to use both of them :)

15. iop360

oh ok

16. zepdrix

|dw:1349559254725:dw|

17. iop360

hey , i got it, thanks!

18. zepdrix

Yayyy iop \:D/

19. iop360

:D thnks for helping