## iop360 Group Title isolate y for the following equation: one year ago one year ago

1. iop360 Group Title

$x= -14e ^{2-y} + y^3 + 7y + 6$

2. ByteMe Group Title

i don't think there is an elementary method to do that.

3. iop360 Group Title

hmm the original equation asks to find the inverse function of $-14e ^{2-x} + x^3 + 7x + 6$

4. iop360 Group Title

which means swapping y for x and solving for y

5. iop360 Group Title

and then find the equation of the line perpendicular to this inverse function at x = 14

6. ByteMe Group Title

correct... but isolating the y after you reversed it is very difficult. i guess all you could do here is give the function implicitly.

7. ByteMe Group Title

can you give the original problem? looks like you need to take derivative implicitly here.

8. iop360 Group Title

differentiate both sides of the equation, find y' maybe

9. iop360 Group Title

ok

10. iop360 Group Title

let $f(x) = -14e ^{2-x} + x^3 + 7x + 6$ find an equation of the normal line to the graph of f-1(x) at the point on the graph where x=14

11. iop360 Group Title

normal line btw, means the line w/ a negative reciprocal

12. iop360 Group Title

aka perpendicular. And the answer to this is y = -33x+464

13. ByteMe Group Title

do you know how the derivatives (slopes) of inverse functions are related?

14. iop360 Group Title

maybe could you state it?

15. iop360 Group Title

i get $\frac{ dy }{ dx } = \frac{ 1 }{ 14e ^{2-y} + 3y^2 + 7 }$

16. iop360 Group Title

my prof gave a hint saying we had to find a value for x that would make the $e ^{2-x}$ part equal to 0. dont know if that helps tho

17. hartnn Group Title

no, need to find the inverse function, u need to find y when x=14 lets say y=2 so u get $$f^{-1}(14)=2$$ then (14,2) is on the graph of x = f-1(y). The slope of that function at that point is what you are looking for.

18. iop360 Group Title

how do we find$f ^{-1}(14)$

19. ByteMe Group Title

since f(2)=14, then f-1(14)=2

20. iop360 Group Title

oh right

21. iop360 Group Title

wasnt 2 just used as a hypothetical

22. hartnn Group Title

yeah, thats a challenge $$14 = -14e ^{2-x} + x^3 + 7x + 6$$ solve for x to get x=2 is not easy

23. hartnn Group Title

i found it by trial and error method

24. iop360 Group Title

oh ok

25. hartnn Group Title

the 1st thing i thought is to eliminate e, by putting x=2 and voila!

26. iop360 Group Title

oh i see

27. hartnn Group Title

so now u have a point, the derivative,can u find the slope of line....and then the equation?

28. iop360 Group Title

yes that makes it way easier

29. iop360 Group Title

thanks to both of you

30. hartnn Group Title

*point and derivative of inverse function....

31. hartnn Group Title

welcome ^_^

32. ByteMe Group Title

yw... also remember you're not looking for the tangent but the normal line

33. hartnn Group Title

i got this because i have seen a similar question here, http://www.physicsforums.com/showthread.php?t=397539

34. iop360 Group Title

i see