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c1-t4t

# c1-t4t - NAME TEST-4T/MAC2311 Page 1 of 5 Read Me First...

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NAME: TEST-4T/MAC2311 Page 1 of 5 Read Me First: Show all essential work very neatly. Use correct notation when presenting your computations and arguments. Write using complete sentences. Be careful. Remember this: "=" denotes "equals" , " " denotes "implies" , and " " denotes "is equivalent to". Do not "box" your answers. Communicate. Show me all the magic on the page. 1. (16 pts.) Fill in the blanks of the following analysis with the correct terminology. Let f(x) = x 4 - 8x 3 . Then f (x) = 4x 3 - 24x 2 = 4(x - 0) 2 (x - 6). Consequently, x = 0 and x = 6 are points of f. Since f (x) > 0 for 6 < x, f is on the set (6, ). Also, because f (x) < 0 when 0 < x < 6 or x < 0, and f is continuous, f is on the interval (- , 6). Using the first derivative test, it follows that f has a(n) at x = 6, and at x = 0. Since f (x) = 12x 2 - 48x = 12x (x - 4), we have f (0) = 0, f (4) = 0, f (x) < 0 when 0 < x < 4, and f (x) > 0 when x > 4 or x < 0. Thus, f is on the interval (0,4), f is on the set (- ,0) (4, ), and f has at x = 0 and x = 4.

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