Answer:
(a) Local Maximum (x,y) = (0,12)
Local Minimum (x,y) = (-9,6) (smaller x-value)
Local Minimum (x,y) = (6,3) (Larger x-value)
(b) Increasing = [tex](-9,0)\cup (6,\infty)[/tex]
Decreasing = [tex](\infty,-9)\cup (0,6)[/tex]
Step-by-step explanation:
(a)
Local Maximum: The function gives maximum value in small neighborhood.
From the given graph it is clear that the maximum value of the function is 12 at x=0. So,
Local Maximum (x,y) = (0,12)
Local Minimum: The function gives minimum value in small neighborhood.
It is clear that the minimum value of the function is -6 and 3 at x=-9 and x=6. So,
Local Minimum (x,y) = (-9,6) (smaller x-value)
Local Minimum (x,y) = (6,3) (Larger x-value)
(b)
The function is increasing on -9<x<0 and after 6.
Increasing = [tex](-9,0)\cup (6,\infty)[/tex]
The function is decreasing on 0<x<6 and before -9.
Decreasing = [tex](\infty,-9)\cup (0,6)[/tex]
