Now, we will evaluate the second derivative at all the critical points of {{MATH_19}} and apply the second derivative test to determine whether the function {{MATH_20}} has a local extremum at any of those points. {{MATH_21}} {{CMD_22}} Because the value of {{MATH_23}} is {{CMD_24}}{{CMD_25}}positive{{CMD_26}}{{CMD_27}}negative{{CMD_28}}{{CMD_29}}zero{{CMD_30}}{{CMD_31}}, the function {{MATH_32}} has {{CMD_33}}{{CMD_34}}a local maximum{{CMD_35}}{{CMD_36}}a local minimum{{CMD_37}}{{CMD_38}}neither a local maximum nor a local minimum{{CMD_39}}{{CMD_40}}possibly a local maximum, a local minimum or neither{{CMD_41}}{{CMD_42}} at {{MATH_43}} by the second derivative test. {{MATH_44}} {{CMD_45}} Because the value of {{MATH_46}} is {{CMD_47}}{{CMD_48}}positive{{CMD_49}}{{CMD_50}}negative{{CMD_51}}{{CMD_52}}zero{{CMD_53}}{{CMD_54}}, the function {{MATH_55}} has{{CMD_56}}{{CMD_57}}a local maximum{{CMD_58}}{{CMD_59}}a local minimum{{CMD_60}}{{CMD_61}}neither a local maximum nor a local minimum{{CMD_62}}{{CMD_63}}possibly a local maximum, a local minimum or neither{{CMD_64}}{{CMD_65}} at {{MATH_66}} by the second derivative test.