2. Use the graph of y f(x) given below to answer the following questions. List a

Question

2. Use the graph of y f(x) given below to answer the following questions. List all the x values for which f' (x) = 0 List all the x values for which f,(x) DNE ii) i) List all the critical numbers of f(x) iv) List all the interval in which f'(x) 0 vi) List all the local minimum values of f (x) in it .. .........-, , 2 . -4 -2 2 4 -2 exists List all the local maximum values of f(x) in it exists -4 vii) vii) Find the absolute maximum value of (x) in the interval [-3,0] Find the absolute minimum value of (x) in the Interval [0,3] ix)

Explanation / Answer

i) DNE

ii)
x = -2 , -1 and 1

iii)
x = -2 , -1 and 1

iv)
f' < 0 means function decreasing
So, (-inf , -2) U (1 , inf)

v)
f' > 0 --> function f increasing
So, (-2 , 1)

vi)
Local min = -3 when x = -2

vii)
Local max = DNE

viii)
Abs max = 1 when x = 0

ix)
Abs min is -2 when x = 3

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