Question

(a) Can the average rate of change of an increasing function ever be negative?

(b) If the average rate of change of a function between $x=a$and $x=b$is negative, then is the function necessarily decreasing on the interval $(a,b)$?

Short answer

(a) No

(b) Yes

Step-by-step solution

Given Information

(a) The increasing function.

(b) The decreasing function.

Part (a) Step 1: Identify the statement 

The average rate of change of an increasing function is always positive.

Part (b) Step 1: Identify the statement 

If the average rate of change is negative in interval$[a,b]$then function must be decreasing in the same interval.