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 .
The graph above shows the graph of f'(x), the derivative of a function f(x). It is known that f"(-8) = 0 and
f"(1.3) = 0.
(a) Determine the value(s) of x for which f(x) has a relative minimum. Ilustify.
(b) Determine the value(s) of x for which f(x) is increasing. Justify.
(c) Determine the value(s) of x for which f(x) is concave down. Justify.
(d) Is the value of
r(0)-r(-5)
0-(-5)
positive or negative? Use the Mean Value Theorem to justify.
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