anyone with a TI-89 check this for me?

Question

Anyone with a TI-89 check this derivative for me?
i tried to download a program to find derivatives on a TI-83 plus but my calc doesnt connect.
someone iwth a TI-89 check this for me?
f(x)= ((x-sqrt(x))/(x+sqrt(x)))^2

evaluate at x=1
is it 0 at f '(1)?

Answer 1

That's a pretty nasty one.

Using quotient rule and chain rule:

f'(x) = 2((x - √x)/(x + √x))[(x + √x)(1 - 1/(2√x)) - (x - √x)(1 + 1/(2√x))]/(x + √x)²

f'(1) = 2((1 - 1)/(1 + 1))[(1 + 1)(1 - 1/2) - (1 - 1)(1 + 1/2)]/(1 + 1)²
= 2(0/2)(-1 - 0)/4
= 0

So yes, I agree, f'(1) = 0.

Answer 2

No TI89 but the derivative (using Maple) is 2*(x-x^(1/2))*x^(1/2)/(x+x^(1/2))^3 which is equal to 0 at x=1. You have to be a little careful using the numerical derivative "nDeriv" on the calculator to find where f'=0. There are roudning issues.

Answer 3

Try to double click on it. That works sometimes so me, but just check over a time by waving the mouse over the batery icon and it is bound to show up :]