Consider the function f(x) = x*el8. For this function there are three important intervals: (– 00, A],. [A, B], and [B, 0) where A and B are the critical numbers. Find A and B For each of the following intervals, tell whether f(x) is increasing (type in INC) or decreasing (type in DEC). (- 00, A]: [A, B]: [B, ∞)

Consider the functions f: [7] to [9].  How many of these functions have a range of {5,6}?

Identify where the function f(x) = x³ – 4x? + 8x + 1 is increasing, decreasing, concave up, and concave down. (Give your answer as an interval in the form (*,*). Use the symbol o for infinity, U for combining intervals, and an appropriate type of parentheses "(",")", "[", or "]" depending on whether the interval is open or closed. Express numbers in exact form. Use symbolic notation and fractions where needed. Enter DNE if no such interval exists.) f is increasing on: f is decreasing on: f is concave up on: f is concave down on: Use the graphing utility to graph f. f(x) = 20 y + 10 -20 -10 10 20 -10 powered by Sousep -20

Consider the following model to grow simple networks. At time t = 1 we start with a complete network with no = 6 nodes. At each time step t > 1 a new node is added to the network. The node arrives together with m = 2 new links, which are connected to m = 2 different nodes already present in the network. The probability II, that a new link is connected to node i is: N(t-1) II¿ = ki - 1 Ꮓ with Z=(k-1) j=1 where ki is the degree of node i, and N(t - 1) is the number of nodes in the network at timet - 1.