HW7 - derivative. Problem 5. Let f ( x ) = xe x . Find f (...

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MATH 102, ASSIGNMENT 7 DUE JULY 21 Problem 1. i) Find the domain of f ( x ) = ln ( ln x ) . ii) Write the equation of the tangent line to the graph of f ( x ) = ln x 2 + x + 2 x + 3 at x = 1. Problem 2: Consider the function f ( x ) = - 1 + 2ln x x 2 . a) What is the domain of f ? b) Find the critical numbers and the points of inflection for f . c) Find the absolute extrema of f on the interval [ e , e 2 ] . Problem 3: Consider the function f ( x ) = x e - e x . What kind of relative extrema are f ( 1 ) and f ( e ) ? (Hint: Second-Derivative Test!) Problem 4. Sketch the graph the function f ( x ) = e - x 2 / 2 by going through the “5-step” plan: domain, intercepts, asymptotes, first derivative, second
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Unformatted text preview: derivative. Problem 5. Let f ( x ) = xe x . Find f ( 2009 ) ( ) . Problem 6. Find the point of inection for the logistic function P ( t ) = KP e rt K + P ( e rt-1 ) . Problem 7. Consider the function f ( x ) = x x for x > 0. a) Put f ( x ) in the form e g ( x ) for a suitable function g ( x ) . b) Find f ( 1 ) . J-RULE: Just answers - yes, 5 - wont get you full marks, but (correctly) justied answers - yes, because. .., (some algebra). .. (sweat sweat) . .. 5 - will. 1...
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