Question

On a coordinate plane, a curved line with minimum values of (negative 0.5, negative 7) and (2.5, negative 1), and a maximum value of (1.5, 1), crosses the x-axis at (negative 1, 0), (1, 0), and (3, 0), and crosses the y-axis at (0, negative 6).

Which interval for the graphed function contains the local maximum?

[–1, 0]
[1, 2]

Answer 1

The interval for the graphed function that contains the local maximum is [1, 2].

Since the problem states that the curve has a local maximum at (1.5, 1), we know that the curve must be increasing to the left of this point and decreasing to the right of this point.

The curve crosses the x-axis at (-1, 0), (1, 0), and (3, 0), so the interval [1, 2] is the only interval that is to the left of (1.5, 1) and to the right of a point where the curve crosses the x-axis. Therefore, the local maximum must occur within the interval [1, 2].