Question: Graph the fourth degree polynomial for various values of the constant a. (a) Determine the values of a for which p has exactly one relative

Graph the fourth degree polynomial

p(x) = x4 + ax + 1

for various values of the constant a.

(a) Determine the values of a for which p has exactly one relative minimum.

(b) Determine the values of a for which p has exactly one relative maximum.

(c) Determine the values of a for which p has exactly two relative minima.

(d) Show that the graph of p cannot have exactly two relative
extrema.

p(x) = x4 + ax + 1

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