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Unformatted text preview: '( x ) = 2 x c) Use the Slope Criterion to determine the stability of the equilibria (2 pts) f '(0) = 0 = 0 <1 So x* = 0 is STABLE f '(1) = 2 = 2 >1 So x* = 1 is UNSTABLE EXTRA CREDIT (2 pts) Find the derivative of the following function at x=2 f ( x ) = x cos( px ) x 2 METHOD 1: Simplify: f ( x ) = cos( px ) x f '( x ) = x ( sin( px ) p )  cos( px ) x 2 f '(2) = 2(0)  1 4 = 1 4 METHOD 2: (More complicated, but works out) f '( x ) = x 2 x sin( px ) ( ) p + cos( px ) [ ]x cos( px ) 2 x x 4 f '(2) = 2 2 2(0) p +1 [ ] 2(1) 2(2) 2 4 = 4  8 16 = 1 4...
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 Spring '08
 Johnson
 Calculus, Logic, Derivative

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