Question: Consider the general cubic polynomial f(x) = x 3 + ax 2 + bx + c, where a, b, and c are real numbers. a.

Consider the general cubic polynomial f(x) = x3 + ax2 + bx + c, where a, b, and c are real numbers.

a. Show that f has exactly one inflection point and it occurs at x* = -a/3.

b. Show that f is an odd function with respect to the inflection point (x*, f(x*)). This means that f(x*) - f(x* + x) = f(x* - x) - f(x*), for all x.

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