Original
Now we know that {{MATH_14}} is {{CMD_15}}{{CMD_16}}increasing{{CMD_17}}{{CMD_18}}decreasing{{CMD_19}}{{CMD_20}} so since {{MATH_21}}
{{CMD_22}}
{{CMD_23}}{{MATH_24}}.{{CMD_25}}
{{CMD_26}}{{MATH_27}}.{{CMD_28}}
{{CMD_29}}
We use these bounds to find that
{{MATH_30}}
Thus our estimate from the linear approximation of {{MATH_31}} can be off by at most {{MATH_32}}.