For any constant c, define the function f-subscript c withe formula f-subscript c(x)= x^3 + 2x^2 + cx
a)graph y= f-subscript c(x) for these values of the parameter c: c = -1,0,1,2,3,4. What are the similarity and differences among the graphs, and how do the graphs change as the parameter increases?
b) For what values of the parameter c will f-subscript c have one local maximum and one local minimum? use calculus. As c increases, what happens to the distance between the local maximum and local minimum?
c)for what values of the parameter c will f-subscript c have no local maximum or local minimum?use calculus.
d)are there any values of the parameter c for which f-subscript c will have exactly one horizontal tangent line?
i need the answer to the questions to be explanations including what rules you used and any steps involved. really appreciate it thanks in advance.