what does a negative average rate of change indicate about a function over an interval?\n a. the function is…
what does a negative average rate of change indicate about a function over an interval?\n a. the function is decreasing.\n b. the function is constant.\n c. the function is increasing.\n d. the function is undefined.
Answer
Explanation:
Step1: Recall the definition 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)<0) (since (x_2>x_1) for a non - degenerate interval). This means (f(x_2)<f(x_1)). When (x_2>x_1) and (f(x_2)<f(x_1)), the function is decreasing over the interval ([x_1,x_2]).
Answer:
a. The function is decreasing.