10ABA2

# 10ABA2 - MATH 10A Bonus Assignment 2(Section B0 Name Due...

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MATH 10A Bonus Assignment 2 Name (Section B0 ) Due March 11, 3:50pm in class. This assignment is worth up to 4 points on your Midterm 2 score. You may get help with these problems, but the solution should be written by you in your own words. Ex- plain your solution clearly. You are encouraged to use the midterm solutions as a guide. Problem 1: Let f ( x ) = 4 x 3 + 6 x 2 - 24 x + 7. (a) Find intervals where f is increasing. (b) Find intervals where f 0 is increasing. Solution: (a) To ﬁnd where f is increasing, ﬁnd where f 0 is positive. We have f 0 ( x ) = 12 x 2 + 12 x - 24 = 12( x 2 + x - 2) = 12( x - 1)( x + 2) . Solving f 0 ( x ) = 0 gives x = - 2 , 1. Consider the test points - 3 , 0 , 2 in the following regions ............................................................................................................................................................................................................................................................................................. | | -

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