Question

3. (16 points) (a) The graph of f(z) is given below. Using the graph, determine each of the following: i) 2-coordinate of local maxima ii) D-coordinate of local minima iii) open interval(s) on which is INCREASING between 1 = A and 2 =D iv) open interval(s) on which f is DECREASING between 2 = A and 1=D v) open interval(s) on which f is CONCAVE UP between 1 = A and z =D vi) open interval(s) on which f is CONCAVE DOWN between 3 = A and 1=D vii) D-coordinate of inflection point(s) off XA XD 3 2 XaB (b) Sketch one curve f(x) with the following properties: i) Continuous on (-5,7) ii) Absolute maximum at r=-5 iii) Decreasing on (-5, -3) iv) Local maximum at I = 0 v) Inflection point at <= 3 vi) Absolute minimum at = 5 Be sure to label all points.

Answer 1

의 local maximum (increases and then decreases) 2.5 + s local minianum (decreases and then increases) > XL B,C -1.75 1.75 $ Increases (6, o) u (6,0) (-1.5 =))) (125, 1-5) f decreases as (A,B) U(0,0) |(-2.5, -1.75) 310,1.75) > Concave uss > > 0 (A-1) U (1,0) » ||-2-5, 1) U (1,2-5) Con Cave down f"(x) e o » (1,1) Inflection point al - fl-1) = f(i) -S | (-1,-5) and (1.-5) 10.-))