# hw 5 soln - Calculus for the Life Science I MAT1330A ,...

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Unformatted text preview: Calculus for the Life Science I MAT1330A , MAT1330B, MAT1330E Assignment 5 Question 1 Consider the function f ( x ) = x 5 / 3 e − x . a ) Find the roots of f to complete the following table. x x < x > f ( x )- + root b ) Compute the derivative of f . f ′ ( x ) = parenleftbigg d d x x 5 / 3 parenrightbigg e − x + x 5 / 3 parenleftbigg d d x e − x parenrightbigg = 5 3 x 2 / 3 e − x- x 5 / 3 e − x = x 2 / 3 parenleftbigg 5 3- x parenrightbigg e − x c ) Find the critical points of f to complete the following table. x x < < x < 5 / 3 5 / 3 x > 5 / 3 f ′ ( x ) + +- increasing increasing local max. decreasing d ) Compute the second derivative of f . Since f ′ ( x ) = parenleftbigg 5 3 x 2 / 3- x 5 / 3 parenrightbigg e − x , we get f ′′ ( x ) = parenleftbigg d d x parenleftbigg 5 3 x 2 / 3- x 5 / 3 parenrightbiggparenrightbigg e − x + parenleftbigg 5 3 x 2 / 3- x 5 / 3 parenrightbiggparenleftbigg d d x e − x parenrightbigg = parenleftbigg 10 9 x − 1 / 3- 5 3 x 2 /...
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## This note was uploaded on 04/08/2010 for the course MATH MAT1330 taught by Professor Rad during the Spring '10 term at University of Ottawa.

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hw 5 soln - Calculus for the Life Science I MAT1330A ,...

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