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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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