Calculus-Sec-3-1-Solution


3.1    Definition of Derivatives, Differentiation   by SGLee - HSKim, YJLim

                                                                                                             http://youtu.be/7wTBWuk2CzU

1-7. Differentiate each of the following functions using Definition 3.1.1, if it exists.

 

1. 

 

 

      

             




2. 

 

       

               




3. 

 

 

      

              




4. 

 

 

      

             

             




5. 

 

 

     

            

            




6. 

 

 

    

           

           




7. 

 

      

              




8. Is the function  differentiable at ?

 

     

      Hence  is differentiable at  and .




9. Discuss a geometric and physical interpretation of .

 

 

      1. Geometric interpretation: The slope of the tangent to the curve at a point is equal to the derivative

           derivative of the function at that point.

      2. Physical interpretation: The average velocity is the ratio between distance travelled () and the time elapsed ().




    

 

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