14. what does a positive average rate of change indicate about a function over an interval?\na. the function…
14. what does a positive average rate of change indicate about a function over an interval?\na. the function is decreasing.\nb. the function is undefined.\nc. the function is constant.\nd. the function is increasing.
Answer
Explanation:
Step1: Recall the concept of average rate of change
The average rate of change of a function (y = f(x)) over an interval ([x_1,x_2]) is given by (\frac{f(x_2)-f(x_1)}{x_2 - x_1}).
Step2: Analyze the sign of the average rate of change
If the average rate of change (\frac{f(x_2)-f(x_1)}{x_2 - x_1}>0), then (f(x_2)-f(x_1)) and (x_2 - x_1) have the same sign. When (x_2>x_1) (i.e., (x_2 - x_1>0)), then (f(x_2)>f(x_1)). This means that as (x) increases, (y = f(x)) also increases.
Answer:
d. The function is increasing.