Determining the conditions such that the graph f resembles the given graph

Question

I am pretty stuck on these problems, as I am not even sure where to really start with them.

In Exercises 65–70, determine conditions for the coefficients of $$f(x)=ax^3+bx^2+cx+d$$ such that the graph of $f$ resembles the given graph.

I would really appreciate it if someone could help me through 65 and 66, and I'm not so much concerned with finding the answer as I am trying to understand what the question is even looking for.

Answer 1

The question is asking to find the set $\{a,b,c,d\}$ such that the graph has that shape.

Answer 2

Hint: In both cases, you know the inclination of the tangent to the graph in $x=0$; namely, $\pm45^\circ$ in the first two cases, and $0$ or $\pm180^\circ$ in the latter two. Now, can you tell me what calculus-related notion represents the geometrical tangent to a function's graph ? ;-$)$