- (C) At x = 1 and 3, f ′(x) = 0; therefore f has horizontal tangents.
For x < 1, f ′ > 0; therefore f is increasing.
For x > 1, f ′ < 0, so f is decreasing.
For x < 2, f ′ is decreasing, so f ′′ < 0 and the graph of f is concave downward.
For x > 2, f ′ is increasing, so f ′′ > 0 and the graph of f is concave upward.