Answer:
Local max: (2, 0)
Local min: (-2, -4) and (6, -8)
Step-by-step explanation:
For this problem, we simply need to understand the idea of maximums and minimums within a graph. A maximum occurs when the graph reaches a peak y-value in comparison to the rest of the function on the graph. A minimum occurs when the graph reaches a "lowest" y-value in comparison to the rest of the function on the graph.
In the given graph, let's work from left to right. Notice how on the left, our trace goes from (-8,-4) to (-2, -4) before there is any change in the function. As there is an increase in the function, there is a pivot at which the function begins to decrease at (2,0). Notice at this point, there is a "peak" which we will call a maximum. As the function continues to decrease we see it leave the graphed space at the point (6, -8) which is a "lowest" peak for our graph. We can consider this to be a minimum.
With this graph, you could argue that there is 1 local/absolute maximum, and 2 local but 1 absolute minimum. To the left of the y-axis, we have a maintained local minimum at x = -4. To the right of the y-axis, we have an infinite decrease that we cannot compute visually after (6, -8). This point can be considered both a local and absolute minimum. The point (2, 0) is the "peak" of the graph in that there is no other value of the function higher than when the function is at (2, 0). This means it is both a local and absolute maximum.
I hope this helps.
Cheers.
