Original
Here we have unlabeled graphs of {{MATH_233}}, {{MATH_234}}, and {{MATH_235}}:
{{CMD_236}}
{{ENV_237}}
{{CMD_238}}
Identify each curve above as a graph of {{MATH_239}}, {{MATH_240}}, or {{MATH_241}}.
{{CMD_242}}
Here we see three curves, {{MATH_243}}, {{MATH_244}}, and {{MATH_245}}. Since {{MATH_246}} is
{{CMD_247}}{{CMD_248}}positive{{CMD_249}}{{CMD_250}}negative{{CMD_251}}{{CMD_252}}increasing{{CMD_253}}{{CMD_254}}decreasing{{CMD_255}}{{CMD_256}} when {{MATH_257}}
is positive and
{{CMD_258}}{{CMD_259}}positive{{CMD_260}}{{CMD_261}}negative{{CMD_262}}{{CMD_263}}increasing{{CMD_264}}{{CMD_265}}decreasing{{CMD_266}}{{CMD_267}} when {{MATH_268}}
is negative, we see
{{MATH_269}}
Since {{MATH_270}} is increasing when {{MATH_271}} is
{{CMD_272}}{{CMD_273}}positive{{CMD_274}}{{CMD_275}}negative{{CMD_276}}{{CMD_277}}increasing{{CMD_278}}{{CMD_279}}decreasing{{CMD_280}}{{CMD_281}}
and decreasing when {{MATH_282}} is
{{CMD_283}}{{CMD_284}}positive{{CMD_285}}{{CMD_286}}negative{{CMD_287}}{{CMD_288}}increasing{{CMD_289}}{{CMD_290}}decreasing{{CMD_291}}{{CMD_292}}, we
see
{{MATH_293}}
Hence {{MATH_294}}, {{MATH_295}}, and
{{MATH_296}}.
{{CMD_297}}
{{CMD_298}}