Question

the graph of a function is given. (a) find all the local maximum and minimum values of the function as well as the value of x at which each occurs. local maximum (x,y)=( ) (smaller x - value) local maximum (x,y)=( ) (larger x - value) local minimum (x,y)=( ) (smaller x - value) local minimum (x,y)=( ) (larger x - value)

Explanation:

Step1: Identify local maximum

A local maximum occurs where the function changes from increasing to decreasing. From the graph, we can see two such points.

Step2: Locate smaller - x value local maximum

The smaller - x value local maximum is at the point where the function first changes from increasing to decreasing. By observing the graph, we find the coordinates.

Step3: Locate larger - x value local maximum

The larger - x value local maximum is the second point where the function changes from increasing to decreasing. By observing the graph, we find the coordinates.

Step4: Identify local minimum

A local minimum occurs where the function changes from decreasing to increasing. From the graph, we can see two such points.

Step5: Locate smaller - x value local minimum

The smaller - x value local minimum is at the point where the function first changes from decreasing to increasing. By observing the graph, we find the coordinates.

Step6: Locate larger - x value local minimum

The larger - x value local minimum is the second point where the function changes from decreasing to increasing. By observing the graph, we find the coordinates.

Assuming we estimate from the graph (since no scale values are given precisely, but we can make rough estimates based on grid - like appearance):
Let's say the local maximum with smaller x - value is approximately (-2, 2), the local maximum with larger x - value is approximately (2, 0). The local minimum with smaller x - value is approximately (-4, - 2), and the local minimum with larger x - value is approximately (0, -3).

Answer:

local maximum (x,y)=( - 2,2) (smaller x - value)
local maximum (x,y)=(2,0) (larger x - value)
local minimum (x,y)=( - 4,-2) (smaller x - value)
local minimum (x,y)=(0,-3) (larger x - value)