The graph of the first derivative of a function f is given below.

Question

https://ibb.co/6JZsyNK question is in this link.

Answer 1

a) The graph of F prime is shown. The intervals in which F prime is increasing is where the graph is positive or above the x-axis. This would be [2,4] and [6, infinity)

b) f has a local maximum when the graph of F prime changes from positive to negative. f has a local minimum when the graph of F prime changes from negative to positive. The local maximum for this graph is at x=4. The local minimums for this graph is at x=2, 6.

c) The graph is f is concave up when the graph of F prime has a visible positive or upward slope. The graph of f is concave down when the graph of F prime has a visible negative or downward slope. Thus, the graph of f is concave up where (1,3) and (5,7) and (8,9) The graph of f is concave down where (0,1) and (3,5) and (7,8)

d) The inflections points of f can be found where the slope of F prime changes, whether from positive to negative or from negative to positive. Thus, the x coordinate of the inflection points of the graph are x=1,3,5,7,8