Week 1: Polynomials – Day 4

Cubic polynomials.

1. Sketch the graph of f(x) = x3.

2. Sketch the graph of g(x) = x(x2 + 1).

Bonus questions: what is the difference between f(x) and g(x), in the neighborhood of x = 0? How many real roots do f(x) and g(x) have?

3. Sketch the graph of h(x) = x(x – 3)2. Hint: how many real roots does h(x) have? What are the values of h(x) around and between the roots?

4. Sketch the graph of p(x) = x(x – 1)(x – 2). Hint: how many real roots does p(x) have? What are the values of p(x) around and between the roots?

5. Sketch the graph of q(x) = -x(x – 1)(x – 2).