Original
Here we have unlabeled graphs of {{MATH_299}}, {{MATH_300}}, and {{MATH_301}}:
{{CMD_302}}
{{ENV_303}}
{{CMD_304}}
Identify each curve above as a graph of {{MATH_305}}, {{MATH_306}}, or {{MATH_307}}.
{{COMMENT_308}}
{{COMMENT_309}}
{{CMD_310}} {{COMMENT_311}}
Here we see three curves, {{MATH_312}}, {{MATH_313}}, and {{MATH_314}}. Since {{MATH_315}} is
{{CMD_316}}{{CMD_317}}positive{{CMD_318}}{{CMD_319}}negative{{CMD_320}}{{CMD_321}}increasing{{CMD_322}}{{CMD_323}}decreasing{{CMD_324}}{{CMD_325}} when {{MATH_326}} is
positive and {{CMD_327}}{{CMD_328}}positive{{CMD_329}}{{CMD_330}}negative{{CMD_331}}{{CMD_332}}increasing{{CMD_333}}{{CMD_334}}decreasing{{CMD_335}}{{CMD_336}}
when {{MATH_337}} is negative, we see
{{MATH_338}}
Since {{MATH_339}} is increasing when {{MATH_340}} is
{{CMD_341}}{{CMD_342}}positive{{CMD_343}}{{CMD_344}}negative{{CMD_345}}{{CMD_346}}increasing{{CMD_347}}{{CMD_348}}decreasing{{CMD_349}}{{CMD_350}} and
decreasing when {{MATH_351}} is
{{CMD_352}}{{CMD_353}}positive{{CMD_354}}{{CMD_355}}negative{{CMD_356}}{{CMD_357}}increasing{{CMD_358}}{{CMD_359}}decreasing{{CMD_360}}{{CMD_361}}, we see
{{MATH_362}}
Hence {{MATH_363}}, {{MATH_364}}, and
{{MATH_365}}.
{{CMD_366}}
{{CMD_367}}