for (c), does this help?
- where the first derivative is positive, the graph is increasing. (going up as you move from left to right)
- where the first derivative is negative, the graph is decreasing. (going down as you move from left to right).
- where the first derivative is zero or undefined, you have a critical point. these can be maximums, minimums, inflection points, etc.
- where the second derivative is positive, the graph is concave up (curved like a U or a smile)
- where the second derivative is negative, the graph is concave down (curved like a or a frown)
- if the second derivative is zero, you have a possible inflection point. you can test if this is the case. an inflection occurs if the second derivative changes sign on either side of the point you are concerned with
so drawing a graph based on the table means you have to follow the behavior described by these properties where appropriate