## AravindG 3 years ago find slope at (7,0) using logarithmic differentiation

1. AravindG

|dw:1346421890041:dw|

2. AravindG

i did like this : |dw:1346421919918:dw|

3. AravindG

|dw:1346421955554:dw|

4. AravindG

|dw:1346421991344:dw|

5. Rohangrr

6. AravindG

now when i put x=7 i am stuck!

7. Rohangrr

|dw:1346422078702:dw|

8. AravindG

ya i cant find slope at (7,0)

9. AravindG

10. AravindG

11. AravindG

@satellite73

12. Mikael

Well Ar. I read up on this nice tool Logarithm differentiation. Thx for the news But I can show that it is quite works well here

13. AravindG

how?

14. Mikael

15. AravindG

in btw hapy that i could tell u sthng new :) its very hand for big eqns

16. Mikael

Now WRITE THE SPECIAL CASE of YOURS CAREFULLY with this:

17. Mikael

$(x-7)/(x-2)(x-3)*[ \frac{ 1 }{ x-7 } - \frac{(2x -5)}{(x-2)(x-3)}]$

18. Mikael

Now the FIRST fraction IS REDUCED and the second evaluates to zero at x=7

19. Mikael

$=\frac{ 1 }{ (x-2)(x-3)}$

20. Mikael

= 1/20

21. Mikael

See again my attachment

22. satellite73

the more prosaic way to look at this is when you multiply by the original function the $$x-7$$ cancels

23. Mikael

that's what i said above

24. satellite73

yes, it is nice

25. Mikael

Guru -can you put some explanations whether one has a chance to become YOUR moderatot ?

26. AravindG

gt it !!!! thx a lot @satellite73 and @Mikael