Higher order derivatives and graphs{{CMD_1}}{{PREAMBLE_2}}{{CMD_3}} {{CMD_4}} Here we make a connection between a graph of a function and its derivative and higher order derivatives. {{CMD_5}} {{CMD_6}} {{CMD_7}}{{CMD_8}}{{CMD_9}} We say that a function {{MATH_10}} is {{CMD_11}}increasing{{CMD_12}} on an interval {{MATH_13}} if {{MATH_14}}, for all pairs of numbers {{MATH_15}}, {{MATH_16}} in {{MATH_17}} such that {{MATH_18}} .{{CMD_19}} We say that a function {{MATH_20}} is {{CMD_21}}decreasing{{CMD_22}} on an interval {{MATH_23}} if {{MATH_24}}, for all pairs of numbers {{MATH_25}}, {{MATH_26}} in {{MATH_27}} such that {{MATH_28}} .{{CMD_29}} {{CMD_30}}