Unformatted text preview: stability (b) Draw the updating function and use cobwebbing for h = 2 to illustrate your analysis. (c) Find the value of the parameter h that guarantees the highest harvest. (d) Find the smallest value of the parameter h at which the population goes extinct. Problem 3: [4 points] Give the equation of the tangent line to the curve y = sin(sin( x )) at ( x,y ) = ( π, 0). Problem 4: [6 points] Use the ﬁrst and second order derivatives to sketch the graph of f ( x ) = x + 4 x 2 . You have to ﬁnd the critical points, inﬂexion points, intervals where the function is increasing, . .., and the vertical and horizontal asymptotes if any. Problem 5: [4 points] Find the derivative of the following function. (a) f ( x ) = sin( x 2 )1 tan( x 2 ) , (b) f ( x ) = ln(sin( x 3 ) + 2) . Simplify your answers as much as possible. 1...
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 Spring '08
 DUMITRISCU
 Derivative, Limit of a function, Graph of a function, Allee effect, Prof. SAMINA BASHIR

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