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First derivative test

69 bytes added, 00:17, 4 May 2012
What the test says: combined sign versions
| <math>f</math> is continuous at <math>c</math> and differentiable on the immediate left and immediate right of <math>c</math> || negative || positive || strict local minimum (two-sided) || [[File:Strictlocalminwithderivativezero.png|100px]] [[File:Strictlocalminwithundefinedderivative.png|100px]]
|-
| <math>f</math> is continuous at <math>c</math> and differentiable on the immediate left and immediate right of <math>c</math> || positive || positive || neither local maximum nor local minimum, because <math>f</math> is increasing through the point || [[File:Cubefunctionbasic.png|100px]][[File:Onethirdpower.png|100px]]
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| <math>f</math> is continuous at <math>c</math> and differentiable on the immediate left and immediate right of <math>c</math> || negative || negative || neither local maximum nor local minimum, because <math>f</math> is decreasing through the point ||
|}
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