In both graphs in the left-hand column, {{MATH_9}} is decreasing. In both graphs in the right-hand column, {{MATH_10}} is increasing. What is the difference between the two rows? Their concavity. {{CMD_11}}{{CMD_12}}{{CMD_13}} Let {{MATH_14}} be a function differentiable on an open interval {{MATH_15}}.{{CMD_16}} We say that the graph of {{MATH_17}} is {{CMD_18}}concave up{{CMD_19}} on {{MATH_20}} if {{MATH_21}}, the derivative of {{MATH_22}}, is {{CMD_23}}increasing{{CMD_24}} on {{MATH_25}}.{{CMD_26}} We say that the graph of {{MATH_27}} is {{CMD_28}}concave down{{CMD_29}} on {{MATH_30}} if {{MATH_31}}, the derivative of {{MATH_32}}, is {{CMD_33}}decreasing{{CMD_34}} on {{MATH_35}}. {{CMD_36}} That is, the graph of {{MATH_37}} is concave up if the graph locally lies above its tangent lines, and is concave down if the graph locally lies below its tangent lines.