check\ndetermine where the function is increasing and decreasing and state the coordinates of its…
check\ndetermine where the function is increasing and decreasing and state the coordinates of its extrema.\nthe function is increasing when:\n____________________ and ____________________.\nthe function is decreasing when ______ < x < ______.\nmaximum - ( , )\nminimum - ( , )
Answer
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 $a<x < b$ and $0<x < c$.
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)