Question

which statement is true about the local minimum of the graphed function? over the interval -4,-2, the local minimum is 0. over the interval -2,-1, the local minimum is 25. over the interval -1,4, the local minimum is 0. over the interval 4,7, the local minimum is -7.

Explanation:

Step1: Recall the definition of local minimum

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

Step2: Analyze each interval

• Interval \([-4,-2]\):

Looking at the graph, in the interval \([-4,-2]\), the function has a local minimum value. By observing the \(y -\)coordinates of the points in this interval, we can see that the local minimum is \(0\).

• Interval \([-2,-1]\):

The local minimum in this interval is not \(25\). The value \(25\) is a \(y -\)coordinate of a point \((- 6,25)\) which is not in the interval \([-2,-1]\).

• Interval \([-1,4]\):

The local minimum in this interval is not \(0\). The point \((6,0)\) is not in the interval \([-1,4]\).

• Interval \([4,7]\):

The local minimum in this interval is not \(-7\). The point \((6,-7)\) is not in the interval \([4,7]\).

Answer:

Over the interval \([-4,-2]\), the local minimum is \(0\).