Hello,

I am having so much trouble understanding this problem. I understand (i) and (ii) but don't get why (iii) and (iv) are negative infinity. I tried plugging in a value less than -2 for (iii) for x since it is 1 approaching from the negative side but I keep getting a positive number. When I plug in 0 it gives a negative number. So how do I know if the numerator is going to always be either positive or negative? Also, how do I know the denominator is always going to be positive.

If you could also answer parts b, c, and d.

5. Let f(x) = 202 - 20 - 2 2 2 - x -2 5-x f (2 ) = (x - 1)3 , f"(x) = -2(2 -7) 2 2 - 2x + 1 (20 - 1)2 (2 - 1)4 (a) Find the following limits. (i) lim f (x) (ii) lim f (ac) x - -00 (iii) lim f(x) (iv) lim f(x). (b) Does f have any asymptotes? (c) On what intervals is f increasing? decreasing? At what values of x does f have a local maximum? local minimum? (d) On what intervals is f concave upward? concave downward? Does f have any points of inflection