## anonymous 4 years ago Determine an equation of the line that is tangent to the graph of f(x) = sqrt (x+1) and parallel to x-6y + 4= 0

1. anonymous

I found the derivative , which is the slope is 1/ 2 sqrt (x+1) what do i do next?

2. TuringTest

you need to find when that the derivative is the same as the slope of the given line what is the slope of the given line?

3. lgbasallote

get the derivative of sqrt (x-1)...that's your equation of the tangent

4. TuringTest

what is the slope of x-6y + 4= 0 ?

5. TuringTest

your derivative is wrong, by the way...

6. anonymous

is it.... cuz if it is parallel, i can just plug in that slope to the equation..

7. anonymous

how is it wrong...

8. TuringTest

maybe it's just your notation$\frac d{dx}\sqrt{x+1}=\frac d{dx}(x+1)^{1/2}=\frac12(x+1)^{-1/2}$

9. anonymous

yea..it looks the same i have to solve it by limits

10. TuringTest

we need when that is the same as the slope of the given line. m:$\frac12(x+1)^{-1/2}=m$oh you need the definition, eh? ok...

11. TuringTest

$\frac{\sqrt{x+1+h}-\sqrt{x+1}}h$$=\frac{\sqrt{x+1+h}-\sqrt{x+1}}h\cdot\frac{\sqrt{x+1+h}+\sqrt{x+1}}{\sqrt{x+1+h}+\sqrt{x+1}}$$=\frac{x+1+h-x-1}{h\sqrt{x+1+h}+\sqrt{x+1}}=\frac{h}{h\sqrt{x+1+h}+\sqrt{x+1}}$$=\frac{1}{\sqrt{x+1+h}+\sqrt{x+1}}$which in the limit is$\frac1{2\sqrt{1+x}}$so what have you got for m ?

12. anonymous

umm..isnt the answer of the derivative = the slope?

13. anonymous

and for the line, i got 1/6 as the slope..it looks wrong...i dont know

14. TuringTest

yes, and we want to know when that slope is the same as the slope of the given line$\frac1{\sqrt{x+1}}=\frac16$yes, 1/6 is what I got

15. anonymous

so do i find x using 1/2 sqrt (1+x) = 1/6 ?

16. TuringTest

yes, you need to know the point x for the point-slope form when we make our line

17. anonymous

oh ok thanks!! i got x= 8 :)

18. TuringTest

so now you use the calculus version of point-slope form:$y-y_1=f'(x_1)(x-x_1)$

19. anonymous

don't really get it ..

20. anonymous

do u find a point and then plug in to y2- y1 /x 2- x1 = m?? i got 6y - x + 3 = 0 which is different from the textbook ans