Question

8 1. (30 points) Let f(x) = 2x + - +1. (a) Find the interval(s) where the function is increasing and the interval(s) where it is de- creasing. If the answer cannot be expressed as an interval, state DNE (short for does not exist). (b) Find the relative maxima and relative minima, if any. If none, state DNE. (c) Determine where the graph of the function is concave upward and where it is concave downward. If the answer cannot be expressed as an interval, use DNE. (d) Find the inflection point(s), if any. If none, state DNE.

Let f(x) = 2x + 8/x +1

(a) Find the interval(s) where the function is increasing and the interval(s) where it is decreasing. If the answer cannot be expressed as an interval, state DNE (short for does not exist).

(b) Find the relative maxima and relative minima, if any. If none, state DNE.

(c) Determine where the graph of the function is concave upward and where it is concave downward. If the answer cannot be expressed as an interval, use DNE.

(d) Find the inflection point(s), if any. If none, state DNE

Answer 1

1 0 f(x) = 2x + 1 Domain= ( -1010) f(x) = 2 (1) + 8 1 - 7 1 1 2) to o f'(x) = 28 ज? 3 2x²-8 > 2x² = 8 x² = 4 x= 42 critical points are 3= -21st-2 > 2 3 0 I '(x) positive 0 negative Positive f(x) is increasing on fx, -2) U (2,0). $(x) is decreasing on 42,0) 0 (0,2) 80) 16 13 16 16 --220 there is relative maximum at no 16 16 23o there is relative minimum at una

f(-2) = 2(-2) + f (2) = 212) + ti = 4 + H+) 4+1 { (-2)= (f (2) = 95 4 Relative maximum = Relative minimum (2,-) 16 conave up on 16 30 so concave on ne (01) on (oro) down on "casco concave 16 Concave down for inflection pointe, fl=0 16 there are no inflection pointe inflection pointe a DNE Pleage sate the answer-
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