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Assignment 5 Solutions

# Assignment 5 Solutions - MAT 1330 Fall 2010 Assignment 5...

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MAT 1330, Fall 2010 Assignment 5 Due Wednesday November 17, at the beginning of class. Late assignments will not be accepted; nor will unstapled assignments. Instructor (circle one): Frithjof Lutscher Angelika Welte Aziz Khanchi Robert Smith? DGD (circle one): 1 2 3 4 Student Name Student Number By signing below, you declare that this work was your own and that you have not copied from any other individual or other source. Signature Question 1. For each of the following functions f , ±nd the critical points and classify them; that is ±nd out whether they are local minima, local maxima or neither. Factorize the derivatives. a) f ( x )= 2 3 x 3 7 x 2 24 x +14 Give f ! ( x 2( x + 4)( x +3) . Hence, the critical points of f are x 1 and x 2 (with x 1 <x 2 ) x 1 = 4 and x 2 = 3 . First Method: Calculate f ! ( x 4 x 14 . Find f ! ( x 1 2 .I s x 1 a max or a min? Min FInd f ! ( x 2 2 s x 2 a max or a min? Max Second method: x −∞ x 1 x 2 + f ! ( x ) 0 + 0 f ( x ) # \$ # According to the table: Is x 1 a max or a min? Min Is x 2 a max or a min? Max b) f ( x )=3 −| 16 8 x | . Write the function as f ( x ! 13+8 x if x< 2, 19 8 x if x> 2.

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Assignment 5 Solutions - MAT 1330 Fall 2010 Assignment 5...

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