Determine the largest value of the linear function y = 6x + 3 on the segment [−2; 3] without performing construction.

1. y = 6x + 3 is a straight line with a positive slope, that is, it is a monotonically increasing function on the entire axis. Consequently, it also increases on the segment [-2; 3].

2. By the definition of an increasing function, its value grows with an increase in the value of the argument. Consequently, at the right end of the segment, the value of the function will be greater than on the entire segment. This means that the maximum value of y = 6x + 3 on the segment will have at the point x = 3.

3. Let’s find it:

y = 6 * 3 + 3 = 21

Answer: The largest value of the function y = 21