Decide for each x-value if the function is increasing or decreasing at that poin

Question

Decide for each x-value if the function is increasing or decreasing at that point and if the function is concave up or concave down at that point. Do this by circling the correct responses for each x-value. At x_1 the function is increasing decreasing & concave up concave down At x_2 the function is increasing decreasing & concave up concave down At x_3 the function is increasing decreasing & concave up concave down At x_4 the function is increasing decreasing & concave up concave down Consider the function: f(x) = 2x^3 - 3x. What is the average rate of change of this function between x = -2 and x = 1? At time t in seconds, a particle's distance s(t), in meters, from a point is given in the table. What is the average velocity of the particle from t = 3 to t = 12? (Include proper units and round to two decimal places.) The cost and revenue functions for a company are given. Give the profit function. (Use proper function notation and the proper variable: remember use pi for profit function.) C(q) = 3q + 8000 R(q) = 14q Profit Function: The cost and revenue functions for a company are given. Give the profit function. (Use proper function notation and the proper variables; remember that we use pi for profit function.) C (p) = 15000 - 150p R(p) = p(4000 - 30p) Profit Function: Give the cost, revenue, and profit functions as they pertain to the business described below. Use function notation and q for your variable. Steve pays $819 to start up his business and it costs him $6 to make each stapler. He sells the staplers for $19 each. Profit Revenue: Cost: How many staplers must Steve make and sell to break even?

Explanation / Answer

x1 :
decreasing and concave up
concave up because it is part of a downward facing U

x2 :
increasing and concave up

x3 :
increasing and concave down

x4 :
decreasing and concave down

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14)
f(-2) = 2(-2)^3 - 3(-2) = -10
f(1) = 2 - 3 = -1

Average rate of change = (-10 - (-1)) / (-2 - 1)
= (-10 + 1) / (-3)
= -9/-3
= 3

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