For a twice differentiable function on an interval, a positive second derivative throughout that interval indicates upward concavity (concave up), while a negative second derivative indicates downward concavity (concave down). This corresponds to whether the tangent slope is increasing or decreasing.
Conditions: The function is twice differentiable on the interval under discussion.; The strict sign statement applies where the instantaneous slope-change rate has that sign.
For a twice differentiable function on an interval, a positive second derivative throughout that interval indicates upward concavity (concave up), while a negative second derivative indicates downward concavity (concave down). This corresponds to whether the tangent slope is increasing or decreasing.
Conditions: The function is twice differentiable on the interval under discussion.; The strict sign statement applies where the instantaneous slope-change rate has that sign.