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) = ( )
(b) find the intervals on which the function is increasing, and on which the function is decreasing. (enter your answers using inter
increasing
decreasing

Explanation:

Step1: Identify local maxima

Local maxima occur where the function changes from increasing to decreasing. By observing the graph, we can see the first local - maximum (smaller x - value) and the second local - maximum (larger x - value).

Step2: Identify local minima

Local minima occur where the function changes from decreasing to increasing.

Step3: Determine intervals of increase and decrease

The function is increasing when the y - values are getting larger as x increases and decreasing when the y - values are getting smaller as x increases.

Answer:

(a)
local maximum $(x,y)=( \text{value from graph}, \text{corresponding y - value})$ (smaller x - value)
local maximum $(x,y)=( \text{value from graph}, \text{corresponding y - value})$ (larger x - value)
local minimum $(x,y)=( \text{value from graph}, \text{corresponding y - value})$
(b)
increasing: $(\text{interval from graph})$
decreasing: $(\text{interval from graph})$

Since the graph has no scale and no grid values are given precisely, we can't provide numerical values. But the general process is as above. If we assume a standard grid with unit intervals:
(a)
local maximum $(x,y)=(0, 2)$ (smaller x - value)
local maximum $(x,y)=(3, 4)$ (larger x - value)
local minimum $(x,y)=(1,1)$
(b)
increasing: $(-\infty,0)\cup(1,3)$
decreasing: $(0,1)\cup(3,\infty)$