Posted by **Sean** on Sunday, November 1, 2009 at 7:57pm.

For any constant c, define the function f_c(x)= x^3+2x^2+cx.

(a) Graph y = f_c(x) for these values of the parameter c: c = -1, 0, 1, 2, 3, 4. What are the similarities 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_c have one local maximum and one local minimum? Use Calculus. As c increases, what happens to the distance between the local maximum and the local minimum?

(c) For what values of the parameter c will f_c have no local maximum or local minimum? Use calculus.

(d) Are there any values of the parameter c for which f_c will have exactly one horizontal tangent line?

- Calculus -
**Freddy**, Sunday, November 1, 2009 at 10:28pm
When c changes, the slope of cubic function changes? How is it changing?

- Calculus -
**Sean**, Sunday, November 1, 2009 at 10:30pm
What are the similarities and differences?

## Answer This Question

## Related Questions

- Calculus - For any constant c, define the function f_c(x)= x^3+2x^2+cx. (a) ...
- differential equations - dS/dt = f(S) = kS(1-S/N)(S/M-1) of a fox squirrel ...
- differential equations - dS/dt = f(S) = kS(1-S/N)(S/M-1) of a fox squirrel ...
- please check my math2 - Two bodies hang on a string 2.1m long. The two bodies ...
- Applied Mechanics - Is my work correct? Two bodies hang on a string 2.1m long. ...
- Calculus - Functions? - #1. A cubic polynomial function f is defined by f(x) = ...
- pre calculus - find the following for the function f(x)=(x+3)^2(x-1)^2 a.) find ...
- Calculus - For what values of x is the graph of the function f(x)= x^2e^x ...
- Calculus - If you can helpme on this problem you are GOD. If f(x) = ax^2 + bx + ...
- math pre calculus - find the following for the function f(x)=(x+5)^2(x-2)^2 a....

More Related Questions