Intervals of increase and decrease

Question

Use the graph of f to find the largest open interval on which f is increasing, and the largest open interval on which f is decreasing. (Enter your answers using interval notation.)

(a) Find the largest open interval(s) on which f is increasing. (If two open intervals are equally large enter your answer as a comma-separated list of intervals.) 

 

 

(b) Find the largest open interval(s) on which f is decreasing. (If two open intervals are equally large enter your answer as a comma-separated list of intervals.) 

 

 

Answer 1

Increasing means going up. The largest interval of increasing is [0,3)

The largest interval of decreasing is (3,9)

3 and 9 aren't included in either interval because it changes directions at those points. The slope is 0 - neither increasing or decreasing at x=3 and x=9.