Question

which interval contains a local minimum for the graphed function?
-2, -1
1, 2
2.5, 4
(-0.44, 1.3)
(0.7, 1.7)
(-2.5, 0)
(3.44, 0)

Explanation:

Step1: Understand local minimum

A local minimum is a point where the function value is less than or equal to the values at nearby points.

Step2: Analyze intervals

In the interval [1, 2], the function has a local maximum. In [-2, -1], there is no local minimum. In [2.5, 4], the function is increasing. In the interval around \(x = 3\) (which is in the interval [2.5, 4]), the function has a local minimum at the point \((3,-4)\).

Answer:

[2.5, 4]