Quiz Question - Calculus and Differential Equations

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2022-007

The Fermat Teorem defines that if f had a local maximum or minimum in c, and if f'(c) exists, then f'(c) = 0. A critical number of the function f is a number c in the domain of f where f'(c) = 0 or f'(c) does not exist.

Choose the statement that presents the critical numbers of \(f(x)=x^{3/5}(4-x)\).

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1. 0 and \({2/3}\)
2. \({2/3}\) and \({4/3}\) 
3. \({4/3}\) and \({3/2}\)
4. 0 and \({3/2}\)
5. None of the above.

Original idea by: Rubens de Castro Pereira

Quiz Question - Chapter 04 – The Scale-Free Property

2022-006

Consider scale-free network with k_max = 200 and k_min = 3. Which statement below presents the degree exponent y and its approximate number of nodes N?

1. y = 2 à N ~ 33 
2. y = 2.1 à N ~ 155 
3. y = 2.5 à N ~ 544 
4. y = 3 à N ~ 4344
5. None of the above.

Original idea by: Rubens de Castro Pereira

Quiz Question - Chapter 03 – Random Network

2022-005

Consider the random network below generated according to model G(N, p) with N=8 nodes and average degree <k>=0.7. Each network link was created with the following random numbers:  AB: 0.08, AC: 0.09, CD: 0.4, CF: 0.7, BE: 0.66, AG: 0.01, and EH: 0.9.

Select the option with only the invalid links of the random network generated.

1. AB, EH, AC
2. AG, AB, AC 
3. EH, CD, BE 
4. CF, AG, CD 
5. None of the above.

Original idea by: Rubens de Castro Pereira

Quiz Question - Chapter 02 - Graph Theory – BFS Algorithm

2022-004

Concerning implementing Breadth First Search (BFS) algorithm using a queue, each edge has a length of 1, and the neighbors' order of choice is the biggest number. Observe the oriented graph below.

Suppose you traverse the graph from node 3 to node 1 using BFS, and select the option representing the correct order of all values (node number) loaded in the queue during this operation.

1. 3 – 4 – 6 – 5 – 7 – 8 – 2 – 1 – 10
2. 3 – 6 – 5 – 4 – 8 – 7 – 2 – 1
3. 3 – 4 – 5 – 6 – 2 – 8 – 7 – 10 – 1
4. 3 – 6 – 5 – 4 – 8 – 7 – 2 – 1 – 10
5. None of the above.

Original idea by: Rubens de Castro Pereira