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Unformatted text preview: Math 270 Test 2 Name _________________________ Read and follow all instructions. Try to answer every question; remember, a partially right answer is better than no answer at all. Reduce all fractions to lowest terms. I. Word problems 1. Takeru Kobayashi currently holds a world record for eating 50 hot dogs in 12 minutes. Those 12 minutes can be modeled by x x H ) 944 . ( 100 100 ) ( = where H is the total number of hot dogs eaten after x minutes. Find the AROC of H(x) for x = 5 to x = 10. What does this AROC tell you about Takeru Kobayashi and hot dogs? 2. The number of cats in an alley during the first two months of the year can be approximated by 10 013 . ) ( 2 + + = x x x f where x is the number of day since January 1. a) What does 24 ) 18 ( ≈ f mean in terms of cats in the alley? b) Find ) 2 ( ' f (you may use the power rule). What are the units on your answer? II. Use the graph to number the following quantities from 1 (largest) to 5 (smallest): ___ ) ( ' A f ___the IROC at D ___the AROC from C to E ___the slope at B ___zero III. For each of the following, give the signs of ) ( ' x f and ) ( ' ' x f . 1. 2. 3. x x f ) 9 . 1 ( ) ( = 4. f(x) is the number of pages a boy has left to read in his book after x days of reading, and he is reading faster and faster. x 1 2 3 f(x) 10 11 15 25 A D B C E Math 270 Test 2 IV. Sketch the derivative of the following function. V. Assume f(x) is defined at x = a . State the three things that can make f(x) not differentiable at x = a . Sketch a graph for each one. 1. 2. 3. VI. x x f = ) ( . Use limits to find ) 4 ( ' f . Show your work! You may use the power rule only to check your answer. Math 270 Test 2 Name _________________________ Read and follow all instructions. Try to answer every question; remember, a partially right answer is better than no answer at all. Reduce all fractions to lowest terms....
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 Summer '08
 VAKARIETIS
 Fractions, Derivative, Power Rule, two months, 12 minutes, hot dogs, Takeru Kobayashi

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