1.  Find the values of x for which the graph of f(x) = sin x cos x has a slope of 0 for 0 < x < 2p.

 2.  Find the derivatives:

      a.  f(x) =   3x³ - 4x² + 5x - 1
                                   x²
                       
     b.  

     c.  y = sin x tan x

    d.  f(x) =  sin x
                   cot x

    e.  g(x) = 2 sin²x - csc²x

    f.  y = cos⁷(4x)

    g.  g(x) = 3x⁴ sec (8x)

3.

x	f(x)	g(x)	f '(x)	g '(x)
2	1	4	3	-1
4	4	1	6	-2

 Find the derivatives of the following expressions.

    a.  f(g(x)) at x = 2

    b.  f(x)  at x = 4
         g(x)

    c.  f(x) g(x) at x = 2

    d.  [ f(x)]² - 3g(2x) at x = 2

4.  Find the equation of the two lines through (5,1) that are tangent to y = x².

5.  Find dy/dx  in terms of x for the parametric equations:  x = 3t² - 1
                                                                                           y = cos t

6.  A particle moves along a horizontal line such that its position at any time t ³ 0 is given
     by s(t) = t³ - 6t² + 9t + 1, where s is measured in meters and t in seconds.

     a.  Find any time(s) when the particle is at rest.
     b.  Find any time(s) when the particle changes direction.
     c.  Find any intervals when the particle is moving left.
     d.  Find the total distance the particle travels in the first 2 seconds.
     e.  Find the velocity of the particle when the acceleration is 0.

7.  Derive the derivative formulas we've studied thus far.
 

Answers