Wetzel                                                                        

Math 140

2.1 – The Derivative and the Tangent Line Problem

Review –

            Given the function, 

            graph                  

          Given the function, 

            graph                   

Tangent Line –          

            Find the slope of the function at x = 0.

            Construct the tangent line at x = 0. 

            Def.:  a line that touches a curve at one point and whose slope is equal to that of the curve at that point.

            Ex.:  Find the slope of the function at x = 3.

Differentiation –  (Limit Process)

            The derivative of f(x) at a point c is given by     

            The derivative of f(x) is given by

            Ex.:  Find the derivative by the limit process.

          1.)                

          2.) 

Points where a derivative does not exist  (Not Differentiable)

·        where the graph of f(x) comes to a point

·        where the graph of f(x) has a vertical tangent line

Words/Symbols that imply differentiate.

·        derivative

·        slope at a point

·        instantaneous rate of change

·        velocity

·       

·       

·       

·       

HW:  p.103 #5-9odd, 11, 13, 17