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    • 1.9.17: Derivatives and the Shape of a Graph
      https://phys.libretexts.org/Courses/Georgia_State_University/GSU-TM-Physics_II_(2212)/01%3A_Introduction_to_Physics_Measurements_and_Mathematics_Tools/1.09%3A_Math_Review_of_Other_Topics/1.9.17%3A_Derivatives_and_the_Shape_of_a_Graph
      let f be a continuous function over an interval I containing a critical point c such that f is differentiable over I except possibly at c; if f′ changes sign from positive ...let f be a continuous function over an interval I containing a critical point c such that f is differentiable over I except possibly at c; if f′ changes sign from positive to negative as x increases through c, then f has a local maximum at c; if f′ changes sign from negative to positive as x increases through c, then f has a local minimum at c; if f′ does not change sign as x increases through c, then f does not hav…
    • 1.9.17: Derivatives and the Shape of a Graph
      https://phys.libretexts.org/Courses/Georgia_State_University/GSU-TM-Physics_I_(2211)/01%3A_Introduction_to_Physics_Measurements_and_Mathematics_Tools/1.09%3A_Math_Review_of_Other_Topics/1.9.17%3A_Derivatives_and_the_Shape_of_a_Graph
      let f be a continuous function over an interval I containing a critical point c such that f is differentiable over I except possibly at c; if f′ changes sign from positive ...let f be a continuous function over an interval I containing a critical point c such that f is differentiable over I except possibly at c; if f′ changes sign from positive to negative as x increases through c, then f has a local maximum at c; if f′ changes sign from negative to positive as x increases through c, then f has a local minimum at c; if f′ does not change sign as x increases through c, then f does not hav…

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