Saturday
April 19, 2014

Homework Help: Calculus

Posted by Sean on Sunday, November 1, 2009 at 10:36pm.

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?

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