Question

Which best describes the graph of the cubic function f(x) = x3 + x2 + x + 1?

As x increases, y increases along the entire graph.
As x increases, y decreases, increases, and then decreases again.

Answer 1

"As x increases, y increases along the entire graph."

Reason: f'(x) = 3x^2 + 2x + 1. Its discriminant is 4 - 12 = -8 < 0, so f'(x) > 0 for all x. Thus f is strictly increasing everywhere (no local maxima or minima).