Question

check
determine where the function is increasing and decreasing and state the coordinates of its extrema.
the function is increasing when:
__________________ and __________________.
the function is decreasing when ____ < x < ____.
maximum - ( , )
minimum - ( , )

Explanation:

Step1: Recall increasing - decreasing rules

A function is increasing when the slope is positive and decreasing when the slope is negative. Extrema occur where the slope changes sign.

Step2: Identify increasing intervals

Looking at the graph, the function is increasing from the x - value of point A to the x - value of point B and from the x - value of point O to the x - value of point C. Let's assume the x - coordinate of A is $a$, B is $b$, O is $0$ and C is $c$. The function is increasing when $a

Step3: Identify decreasing interval

The function is decreasing between the x - value of point B and the x - value of point O. So it is decreasing when $b < x <0$.

Step4: Locate maximum

The maximum occurs at point B. If the coordinates of B are $(b,y_{B})$, the maximum is $(b,y_{B})$.

Step5: Locate minimum

The minimum occurs at point O. If the coordinates of O are $(0,0)$, the minimum is $(0,0)$.

Answer:

The function is increasing when: $a < x < b$ and $0 < x < c$.
The function is decreasing when $b < x <0$.
Maximum - $(b,y_{B})$
Minimum - $(0,0)$

(Note: In a real - world scenario, you would need to determine the exact values of $a$, $b$, $c$ and $y_{B}$ from the graph's scale)