27. Exercises 25 − 36 refer to Fig. 23 , which contains the graph of f ' ( x ) the derivative of function f ( x ) . Explain why f ( x ) has a relative maximum at x = 3 .
27. Exercises 25 − 36 refer to Fig. 23 , which contains the graph of f ' ( x ) the derivative of function f ( x ) . Explain why f ( x ) has a relative maximum at x = 3 .
Exercises
25
−
36
refer to Fig.
23
, which contains the graph of
f
'
(
x
)
the derivative of function
f
(
x
)
.
Explain why
f
(
x
)
has a relative maximum at
x
=
3
.
Formula Formula A function f(x) attains a local maximum at x=a , if there exists a neighborhood (a−δ,a+δ) of a such that, f(x)<f(a), ∀ x∈(a−δ,a+δ),x≠a f(x)−f(a)<0, ∀ x∈(a−δ,a+δ),x≠a In such case, f(a) attains a local maximum value f(x) at x=a .
Suppose that the first derivative of y = ƒ(x) is y' = 6(x + 1)(x - 2)2. At what points, if any, does the graph of ƒ have a local maximum, local minimum, or point of inflection?
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