James W.

# using f(x)=1/sqrtx, find a tangent line that is parallel to x+2y+6=0

I can get most of the way through this problem.  I know the tangent line is y=-1/2x+3/2.  I know it intersects the function at (1, 1).  I get stuck when trying to prove it.  using the formula:

limit  of (f(c+deltax)-f(c))/deltax as deltax approaches 0

I put my funciton into the formula and remove the fraction from the top.  Then, I multiply by the conjugate.  Then, i Simplify and I am left with:

-1/(sqrtx)(sqrt(x+deltax))(sqrtx+sqrt(x+deltax))

That is where I am stuck.  So, my questions is:  How do I get to (y=-1/2x+3/2) from here?  As always please be as specific as possible.  Thank you so much for your help.

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