Question

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

Explanation:

Step1: Recall rate - of - change concept

The rate of change of y with respect to x is related to the slope of the function. The steeper the slope of the curve of y vs x, the faster y is changing.

Step2: Analyze intervals visually

Visually, on a graph, the interval where the function has the steepest positive - slope is the interval where y is increasing the fastest. In a typical upward - sloping then downward - sloping curve (like a parabola opening downwards), the steepest positive slope occurs before the vertex. Usually, the middle of the upward - sloping part of the curve has the steepest positive slope. Among the given intervals, the interval between x = 1 and x = 3 is likely to have the steepest positive slope compared to the other intervals.

Answer:

between x = 1 and x = 3