Concavity: correction to the diagram In the concave-down panel, $f'$ is decreasing and \(f''

Question

Concavity: correction to the diagram

In the concave-down panel, $f'$ is decreasing and $f''<0$. The printed $f''>0$ in that panel is a sign error. Concave up corresponds to an increasing gradient and $f''>0$.

Accepted Answer

Concave upwards: $f'(x)$ increases and $f''(x)>0$; the graph is increasing at an increasing rate or decreasing at a decreasing rate. Concave downwards: $f'(x)$ decreases and $f''(x)<0$; the graph is increasing at a decreasing rate or decreasing at an increasing rate.

Linear Regression Summary Note (Concavity or Curvature)

Linear Regression Summary Note (Concavity or Curvature)

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