Answer: The required answers are
(a) Local minimum over the interval (-3, 0] is x = -1.25 and the minimum value is -16.
(b) Local maximum over the interval [0, 3] is x = 1 and the maximum value is 4
and
(c) Local minimum over the interval [0, 5) is x = 2.5 and the minimum value is -3.
Step-by-step explanation: We are given to use the graph to find the following local maximum and local minimum of the given function :
(a) Local minimum over the interval (-3, 0],
(b) Local maximum over the interval [0, 3]
and
(c) Local minimum over the interval [0, 5).
(a) From the graph, we see that over the interval (-3, 0], the minimum point of the curve is (-1.25, -16).
So, the local minimum of the given function over the interval (-3, 0] is x = -1.25 and the minimum value is -16.
(b) From the graph, we see that over the interval [3, 0], the maximum point of the curve is (1, 4).
So, the local maximum of the given function over the interval [3, 0] is x = 1 and the maximum value is 4.
(c) From the graph, we see that over the interval [0, 5), the minimum point of the curve is (2.5, -3).
So, the local minimum of the given function over the interval [0, 5) is x = 2.5 and the minimum value is -3.
Thus, the required answers are
(a) Local minimum over the interval (-3, 0] is x = -1.25 and the minimum value is -16,
(b) Local maximum over the interval [0, 3] is x = 1 and the maximum value is 4
and
(c) Local minimum over the interval [0, 5) is x = 2.5 and the minimum value is -3.