Question

my book says the derivative of y=x^1/2 is a function with domain (0,infinity). However, the function x^1/2 has a domain [0,infinity), so it could have a right-hand derivative at x=0. Prove that it does not

Answer 1

a derivative is a limit .... define it in terms of its limit

Answer 2

\[\lim_{x\to 0^+}\frac{\frac{1}{x+h}-\frac1x}{h}\]
does it exist?

Answer 3

and why would you say that the function 1/x has 0 in its domain?

Answer 4

sorry, book said \[\sqrt{x}\]

Answer 5

... sqrt(0) is acceptable then

Answer 6

the derivative of sqrt(x) is a limit process ... etc :)