Question

Need help answering this problem

Answer 1

(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 =
`(-9,0)\cup (6,\infty)`

Decreasing =
`(\infty,-9)\cup (0,6)`

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 =
`(-9,0)\cup (6,\infty)`

The function is decreasing on 0<x<6 and before -9.

Decreasing =
`(\infty,-9)\cup (0,6)`