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)=() local minimum (x,y)=() (smaller x - value) local minimum (x,y)=(2,2) (larger x - value)

Explanation:

Step1: Identify local maximum

A local maximum is a point where the function changes from increasing to decreasing. By observing the graph, we can see that the local maximum occurs at the point where the curve changes its upward - moving trend to a downward - moving trend.

Step2: Identify local minimum

A local minimum is a point where the function changes from decreasing to increasing. By observing the graph, we can see the local minimum points where the curve changes its downward - moving trend to an upward - moving trend.

Answer:

local maximum $(x,y)=(0, 3)$
local minimum $(x,y)=( - 2,-1)$ (smaller x - value)
local minimum $(x,y)=(2,2)$ (larger x - value)