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# Test3 - Name Calculus Test#3(Chapter 4 1(15 pts a A student...

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Name: __________________________ Calculus Test #3 (Chapter 4) 1. (15 pts.) a) A student was trying to use Newton’s Method to find the root of the function graphed below. No matter what nonzero value the student chose for 1 x , he could never get the right answer. Explain, using the picture below, why the student was never able to get an answer.

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1b) Use Newton’s Method to find the first 2 approximations ( 2 x and 3 x ) of the roots of the equation 5 ) ( 2 - = x x f , using 2 1 = x . Write your answer for 3 x rounded to 4 decimals. 2. (10 pts.) Use Calculus to find the absolute maximum and the absolute minimum values of 5 9 3 ) ( 2 3 + - + = x x x x f on the interval [-3,5].
3. (10 pts.) Sketch the graph of a single continuous function f with domain ( , ) -∞ ∞ such that all of the following hold simultaneously. Note that f is defined for all real numbers including 0 x = . ( ) 0 f x for all x. ( ) 0 f x if 0 x < ( ) 0 f x < if 0 x ( ) 0 f x ′′ if 0 x < ( ) 0 f x ′′ if 0 x 4. (20 pts.) Evaluate the following limits a) 2 0 1 lim x x e x x - -

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b) cos lim x x x π c) x x x 1 0 ) (cos lim +
5. (10 pts.) Your boss asks you to design an open top box with a square bottom. She wants the largest possible volume and wants to use no more than 1,200 in

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Test3 - Name Calculus Test#3(Chapter 4 1(15 pts a A student...

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