Calculus I (16397)
The One-Parameter Family f(x) = x^4 + ax^2
Our discussion of this family includes a solution to problems 3 of Hour Tests II dated 4/5/02 and 11/12/04. In the first case f(x) = 6x^2 - x^4 = - (x^4 - 6x^2) and in the second f(x) = x^4 - 8x^2. Note the graph of y = 6x^2 - x^4 is that of x^4 - 6x^2 reflected about the x-axis.
For an analysis of the information provided by the derivatives f'(x) and f''(x) see
For a sketch of the graph, when a < 0, see