Question

Let. Fox , FO) = * F"(x) = 2XT9 1.Find x-and y-intercepts of the graph of f, if it has any. 2. Find vertical and horizontal asymptote(s) of f, if it has any. 3. Find the critical number(s), intervals(s) of increasing and decreasing and points of relative extrema off, if it has any. 4. Find intervals of concavity and the point(s) of inflection of f, if any Page 2 5. Sketch the graph of f, label all important points from part (1), (2) and (3).

Answer 1

{"cx)= 2(2-3) x 2 123 24 f(r: 21 품 f'(79= 2+2 1._ i intercept put you et 1,0) Y intercept put 2 0 0 Not ty intercept Florie con cretical asymptote 20 Honig onthe asymptoté where 2 = 0 ly Critical points 1 x 2 of increasing and decreasing ( %,O) U (2,0%) de (0,2) increasing relative extrema at a=2 (2, 4) Ang le B 2:21. put fra)= 6 interval tot off 2 I decleasing point of 4. Interval of concavity CD, O) concave down (4026 0, 2) concave down : (2,609 concave up

4 3 (10) + - -4 -2 2 3 4 5 6 -3 -4