6 Marks a Determine if the function f x 9 x 25 2 x 15 is monotonic andor convex

# 6 marks a determine if the function f x 9 x 25 2 x 15

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6 Marks (a)Determine if the function f(x) = 9x2.5– 2x1.5is monotonic and/or convex for 0<x<∞. (b)What is the sum of the following geometric series?4, 20, 100, 500, …, 1562500, 7812500. Page 7 of 9
TERM 1 STANDARD EXAMINATION 2010 1 ( Question 99 MarksConsider the following integer numbers 1, 5, 6, 13, 17, 18, 21, 33, 39, 44, 58, 140, 221. Apply sequential search and binary search algorithms for searching the number 21 and answer the questions below:(a)How many comparisons does sequential search do to find 21? Answer: (3 marks) (b)How many comparisons does binary search do to find 21? Answer: (3 marks) (c)Which algorithm (sequential or binary) is faster? Justify your answer (maximum 3 lines). Question 109 MarksConsider the following weighted graph. Run the nearest-neighbour strategy/algorithm on the graph by starting at vertex 1 and answer the questions below:(a)What is the tour (a cycle through all the vertices) found by the nearest-neighbour algorithm? (b)What is the total weight for the tour found by the nearest-neighbour algorithm? (3 marks) (c)Did the algorithm find the optimum solution (minimum tour)? Justify your answer (maximum 3 lines). Page 8 of 9
TERM 1 STANDARD EXAMINATION 2010 CONCEPTUAL FOUNDATIONS — MATH21001 (3 marks) 11 80 23 7 58 1 7 31 5 13 4 3 1 2 3 4 5 x End of paper N Page 9 of 9