# Thread: question help max and min

1. ## question help max and min

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.

2. Originally Posted by nycmets718
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.
What attempt have you made and where do you get stuck?