Question

If f(x)=x+1/x, find the set of values for which f increases. ( I know that f'(x)=1-1/x^2=0 and x=1, -1. The answer is (-infinity, -1]U[1, infinity) but how can I get there? )

Answer 1

f would be increases when f ' > 0

Answer 2

does that make sense ?

Answer 3

Do you plug -1 and 1 into the original function or the derivative?

Answer 4

the answer should have been (-inf,1) U (1,inf) because at -1 and 1, the function is neither increasing (nor decreasing)

Answer 5

you plug -1 and 1 in f'

Answer 6

looks mine above not complete
f ' > 0
1 - 1/x^2 > 0
(x^2 - 1)/x^2 > 0

(x+1)(x-1)/x^2 > 0

critics point when x=-1, x=0, and x=1

so, just extra information x not equals 0 and (-1Uinf) U (1,inf)

Answer 7

yeah plug in f '

Answer 8

Got it, thanks.

Answer 9

wlcm