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SOMETHINGS' MATHEMATICAL,     TOO


 f(x)  =  e x and the derivative


The exponential function,  f(x) = e x displays a unique property when looking at its derivative.  This exercise help to determine this property.

Procedure:
1.  Graph the natural exponential function,  f(x) = e x.                    expx window         

Use a window corresponding to values in the image.

In MODE change to get 4 places of decimals only.  

2.  Fill in the values for x and e x  in the accompanying table using your calculator.

3.  Fill in the equations for the tangents drawn to f(x) = e x  at each given value of x.
     Use the DRAW menu,  item 5,  to help you get the equations.
     ( TI-82 users get y-intercept values from the table)
 

x

 

y = e x

 

Tangent equation through point

 

slope of line

 

- 3

 

     

- 2

 

     

- 1

 

     

  0

 

     

  1

 

     

  2

 

     

  3

 

     

  4

 

     

4. What is the special property of the function in terms of its derivative?
 





5. The inverse function of f(x) = e is f -1 (x) = ln x.  Fill in the values in the accompanying table. Does this function exhibit a similar property in terms of its derivative?  If so describe it.  If not say why not.

x

 

y = ln x

 

Tangent equation through point

 

slope of line

 

- 3

 

     

- 2

 

     

- 1

 

     

  0

 

     

  1

 

     

  2

 

     

  3

 

     

  4

 

     





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