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Calculus I                                                          Quiz #6                            October 22, 2004

Name____________________                   R.  Hammack                              Score ______
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(1)
Find derivatives of the following functions.
  
(a)  
f(x) = 3x^4 + π x^2 - x + 4
       


(b)   f(x) = x^2/(x + 1)

         



(c)  
f(x) = 3^(1/2) + 1/x^3

        

(2)   If y = x^(1/2), find (d^2y)/dx^2.

        

(3)  
Suppose functions f and g and their derivatives obey the following table.       x          f(x)       f ' (x)    g(x)       g ' (x)    0          0          1           ...  2   1          2          2          -2         3   2          1          -2         -1         5
If    h(x) = 3f(x) + f(x) g(x),    find h ' (2).



(3)   Find the values of x  at which the slope of the tangent to the graph of y = 2x^3 - 3x^2 + 4  is horizontal.