Question

for which values of x is y increasing the fastest? between x = 0 and x = 1 between x = 6 and x = 7 between x = 3 and x = 4 between x = 1 and x = 3

Explanation:

Step1: Recall rate - of - change concept

The rate of change of y with respect to x is given by the slope of the curve. The steeper the curve, the faster y is increasing.

Step2: Analyze slopes in intervals

In the interval between x = 0 and x = 1, the curve has a positive slope but is not very steep. In the interval between x = 6 and x = 7, the curve is decreasing (negative slope). In the interval between x = 3 and x = 4, the curve is near its maximum and has a small positive slope. In the interval between x = 1 and x = 3, the curve has a relatively steep positive slope, so y is increasing the fastest in this interval.

Answer:

between x = 1 and x = 3