Question

assume arrows if no symbols are shown at the ends of the graph. state your answers using interval notation. consider the function graphed below. a. the function has a local maximum of x = \boxed{} at y = \boxed{} b. the function has a local minimum of x = \boxed{} at y = \boxed{} question help: \boxed{} video \boxed{} written example

Explanation:

Part a: Local Maximum

Step1: Identify local maximum point

A local maximum is a point where the function changes from increasing to decreasing. From the graph, the peak (local maximum) occurs at \( x = 0 \) (since the x - coordinate of the highest point in its neighborhood is 0) and the corresponding y - coordinate is 7 (by looking at the grid, the y - value at \( x = 0 \) is 7).

Step1: Identify local minimum point

A local minimum is a point where the function changes from decreasing to increasing. From the graph, the lowest point in its neighborhood (local minimum) occurs at \( x = 6 \) (the x - coordinate of the lowest point in its neighborhood) and the corresponding y - coordinate is 1 (by looking at the grid, the y - value at \( x = 6 \) is 1).

Answer:

For part a: \( x=\boldsymbol{0} \) at \( y = \boldsymbol{7} \)

Part b: Local Minimum