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 "a0"

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"

jamesj · Answer

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

anonymous · Answer

I am clueless.

turingtest · Answer

$$y=5/\sqrt{x} \rightarrow dy/dx=(-5/2)x^{-3/2}$$ 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$$y'(a)=(-5/2)/\sqrt[2]{a^3}$$

turingtest · Answer

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