Question

how do u do that little table to determine intervals on which a function is increasing or decreasing

Answer 1

f'=0 are your critical points; check the results for + or - with a useful value that is within each interval

Answer 2

i found my critical numbers of a f(x)=(x-1)/x^2

Answer 3

the critical numbers are 2 and 0

Answer 4

f' = x(2-x)/x^4 ; good, 0 and 2 are correct :)

Answer 5

plug in values that are inside the intervals to determine the sign of f' inbetween zeros

Answer 6

at x=1; f'(1) = 1

at x=-1; f'(-1) = -3

at x=3 ; f'(3) = -something