Question

Consider f(x)=sqrt(x). Use the definition of the derivative to calculate the derivative of f, then find the slop of the tangent line to the graph of f at the point (4,2). I know the derivative is (1/2)x^(-1/2), but every time I try to get the slope I end up with m=0/0. Help please.

Answer 1

forget the power rule, you are asked to do this by hand

Answer 2

but since you already know the derivative is
\[\frac{1}{2\sqrt{x}}\] you can replace \(x\) by 4 and get \(\frac{1}{4}\)

Answer 3

on the other hand if you have to turn in some paper with your work on it, you will have to compute
\[\frac{\sqrt{x+h}-\sqrt{x}}{h}\] and then take the limit as \(h\to 0\)
what's your choice?

Answer 4

When I do it the longer way showing work I get 0/0. since i get
\[\frac{ \sqrt{4+0}-2 }{0 } \] when I replace h with 0. What did I do wrong here?

Answer 5

should be
\[\lim_{x\to 4}\frac{\sqrt{x}-2}{x-4}\] if you are just finding \(f'(4)\)