The next three questions require you to write intervals using inequalities. To write a single interval you can write a simple inequality like these: X > 3 x < 4 2 < x <4 To include multiple intervals, use "or" to indicate the value could be in either interval, like these: x < 4 or x > 5 x < 2 or 3 < x <6 Given the function f(x) = -2x³- 15x² - 24x + 3, determine the intervals where the function is increasing and decreasing, and the intervals of concavity. Write the intervals using inequalities. f(x) is increasing for: f(x) is decreasing for: f(x) is concave up for: f(x) is concave down for:

Write each pair of inequalities as the intersection of two intervals and graph the result. x1andx7

Shanthie needs to earn at least $500 a week during her summer break to pay for college. She works two jobs. One as a swimming instructor that pays $10an hour and the other as an intern in a law office for$25 hour. How many hours does Shanthie need to work at each job to earn at least $500 per week? (a) Let x be the number of hours she works teaching swimming and let y be the number of hours she worksas an intern. Write an inequality that would model thissituation. (b) Graph the inequality. (c) Find three ordered pairs (x,y) that would be solutions to the inequality. Then, explain what that means for Shanthie.

Elena needs to earn at least $450 a week during her summer break to pay for college. She works two jobs. One as a swimming instructor that pays $9 an hour and the other as an intern in a genetics lab for $22.50 per hour. How many hours does Elena need to work at each job to earn at least $450 per week? (a) Let x be the number of hours she works teaching swimming and let y be the number of hours she works as an intern. Write an inequality that would model this situation. (b) Graph the inequality. (c) Find three ordered pairs (x, y) that would be solutions to the inequality. Then, explain what that means for Elena.