The local minimum is located in the interval (-1, 0). The function is decreasing from negative 1 to 0, which confirms that the local minimum is located in that interval.
The graph you sent is difficult to see, but I can make some generalizations about where the local minimum is likely to be.
A local minimum is a point on the graph where the function value is less than or equal to all the function values in its immediate neighborhood. In other words, it is a point where the function is decreasing on one side and increasing on the other.
Since the graph crosses the x-axis at (negative 4, 0), (negative 3, 0), (negative 1, 0), and (1, 0), we know that the function has a value of 0 at each of these points. Therefore, the local minimum must be somewhere between these four points.
To narrow down the interval where the local minimum is located, we can look at the overall shape of the graph. The graph appears to be decreasing from (negative 4, 0) to (negative 1, 0), and then increasing from (negative 1, 0) to (1, 0). This means that the local minimum is most likely located in the interval **from negative 1 to 0**.
To confirm this, we can calculate the derivative of the function and look for the points where it is equal to 0. The derivative of the function is negative from negative 1 to 0, which means that the function is decreasing in that interval. This confirms that the local minimum is located in the interval **from negative 1 to 0**.
Therefore, the interval for the graphed function that contains the local minimum is **(-1, 0)**.