Question

first up, lets review the assignments learning objectives
get familiar with this topic by reviewing instruction and answering a couple of questions.
question
identify the local maximum and local minimum of the function shown in the graph below.
sorry, thats incorrect. try again?
the local maximum is at $(\boxed{-4},\boxed{6})$ and the local minimum is at $(\boxed{-1},\boxed{1})$

Explanation:

Step1: Recall the definition of local maximum

A local maximum is a point where the function changes from increasing to decreasing. Looking at the graph, the highest point in its local neighborhood is at \(x = - 4\) and \(y=6\).

Step2: Recall the definition of local minimum

A local minimum is a point where the function changes from decreasing to increasing. Looking at the graph, the lowest point in its local neighborhood is at \(x=-1\) and \(y = 1\).

Answer:

The local maximum is at \((-4,6)\) and the local minimum is at \((-1,1)\)