Question

I need help taking this derivative. (It's not particularly hard) but I just can't do it

Answer 1

The problem I'm doing asks me to find the relative extrema for the function \[f(x) = x / \sqrt{x-1}\]

I got the 1st derivative as

And the only critical number as x = 2

Based on the graph, this is correct.

But I just can't accurately take the 2nd derivative.

I tried it and I got

f''(2) should be positive since (2,f(2)) is a relative min. So I took this 2nd derivative incorrectly and I'm not sure why....

Can someone help me please