Using the given graph of y

From the graph you provided, I can visually analyze the extrema of the function $y = f(t)$. Extrema refer to points where the function reaches a maximum or minimum value. Absolute extrema are the highest or lowest points across the entire domain.

Observations:

• The graph shows two distinct points with a curve connecting them.
• The highest point on the curve (maximum) occurs at the peak, and the lowest point (minimum) occurs at the bottom of the curve.

Identifying the extrema:

1. Absolute Maximum: The highest point on the graph seems to occur at $(0, 2)$, where the function value $f(t) = 2$.
2. Absolute Minimum: The lowest point on the graph appears at $(-3, -1)$, where $f(t) = -1$.

These extrema are absolute because no other points exceed the maximum of 2 or fall below the minimum of -1 in the given portion of the graph.

Do you need further details or clarifications about this?
Here are some questions you might consider next:

1. What is the difference between absolute and local extrema?
2. Can a function have more than one absolute maximum or minimum?
3. How does the first or second derivative help in identifying extrema?
4. What role do boundary points play in determining absolute extrema?
5. How can we algebraically verify the extrema when given a function?

Tip: When identifying extrema, always consider the domain of the function, as endpoints may also be candidates for absolute maxima or minima.