The Derivative Homework

Directions: Write legibly and in pencil. Complete the homework on time and by yourself. For each problem, write the instructions, label the solution, show all steps, and write the final answer in a sentence. Do not turn in your scratch work. Staple your pages together, in the correct order, and use this page as a cover sheet.

(1) Using the definition of the derivative, calculate the derivative of the function and then evaluate the derivative function at and

(2) Using the definition of the derivative, calculate the derivative of the function and then evaluate the derivative function at and

(3) Using the definition of the derivative, calculate the derivative if   

(4) Using the definition of the derivative, calculate the derivative if   

(5) Differentiate the function and find the slope of the tangent line at the point where

(6) Differentiate the function and find the slope of the tangent line at the point where

(7) Find the value of the derivative when

(8) Find the value of the derivative when

(9) Use the formula to find the derivative of the function

(10) For each of the following pictures, the graph of and are shown. Label both and .

(11) For each of the following pictures, the graph of and are shown. Label the function and its derivatives for each.

(12) If possible, give an example of a function that is continuous on but does not have a derivative at Sketch and explain.

(13) If possible, give an example of a function that is continuous and increasing on continuous and decreasing on discontinuous at and does not have a derivative at   Sketch and explain.

(14) If possible, give an example of a function that is continuous and increasing on continuous and decreasing on discontinuous at and does not have a derivative at   Sketch and explain.

(15) If possible, give an example of a function that has a graph with an infinite number of points where is not differentiable and is continuous on   Sketch and explain.

(16) Using the definition of the derivative of a function find the derivative function given

(17) Using the definition of the derivative of a function find the derivative function given

(18) Using the definition of the derivative of a function find the derivative function given

(19) Using the definition of the derivative of a function find the derivative function given

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The Derivative Homework
Published by Library of Math -- Online math organized by subject into topics.
Written by Smith, David A.
http://www.libraryofmath.com/the-derivative-homework.html