Quiz (Introducing Derivatives)

Find the derivatives for the given function.

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





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





(3) Explicitly write functions that satisfies the given conditions. Also sketch the graph and explain why the function satisfies the given conditions.

    (a) If possible, give an example of a function that is continuous on but does not have a derivative at Sketch and explain.
    
    (b) If possible, give an example of a function that is continuous and increasing on continuous and decreasing on discontinuous at and has a derivative at   Sketch and explain.
    
    (c) 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.
    
    (d) 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.
    
(4) Using the definition of the derivative of a function find the following derivative functions, if they exist.

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