Question

Find the slope m of the tangent to the curve y = 5 divided by \sqrt{x} at the point where x = a >0

What? I am confused by the "a>0"

Answer 1

because x=0 isn't even in the domain of the function, let alone is the function differentiable there.

Answer 2

I am clueless.

Answer 3

\[y=5/\sqrt{x} \rightarrow dy/dx=(-5/2)x^{-3/2}\] like James says all the a>0 part means is that our function will stay defined for this a, so the slope of the tangent is just\[y'(a)=(-5/2)/\sqrt[2]{a^3}\]

Answer 4

If we allowed the possibility of \[a \le 0\] we would wind up with y'(a) as undefined or imaginary.