Question

For which interval is the average rate of change of f(x) negative? On a coordinate plane, a function starts from above quadrant two and goes through (negative 4, 0) to (negative 3, negative 3). The function then curves upward toward (0, 1) and then curves down toward (3, negative 3). The function then curves up and approaches x = 5. From x = â€"3. 5 to x = â€"1 from x = â€"3 to x = 3 from x = 0 to x = 2. 5 from x = 3 to x = 4. 5.

Answer 1

The interval for which the average rate of change of f(x) is negative is; from x = 0 to x = 2.5.

For the average rate of change of f(x) to be negative, it means that the change in y and the change in x must have opposite signs.

For example, if the change in y is negative, them the change in x must be positive.

Similarly, if the change in y is positive, then change in x must be negative.

Now, the graph showing this quadratic function is missing and so i have attached it.

From the graph, the only interval at which the rate of change for y and x have opposite signs is from x = 0 to x = 2.5.

In this interval, we see that x is increasing from 0 to 2.5 which is positive change while y is decreasing from 1 to -3 which is negative change.

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