For Exercises 67–73 , assume that f is differentiable over ( − ∞ , ∞ ) . Classify each of the following statements as either true or false. If a statement is false, explain why. If f has exactly two critical values at x = a and x = b , where a < b , then there must exist exactly one point of inflection at x = c such that a < c < b . In other words, exactly one point of inflection must exist between any two critical points.
For Exercises 67–73 , assume that f is differentiable over ( − ∞ , ∞ ) . Classify each of the following statements as either true or false. If a statement is false, explain why. If f has exactly two critical values at x = a and x = b , where a < b , then there must exist exactly one point of inflection at x = c such that a < c < b . In other words, exactly one point of inflection must exist between any two critical points.
Solution Summary: The author explains that the provided statement is false because the function f may have more than one inflection point.
For Exercises 67–73, assume that f is differentiable over
(
−
∞
,
∞
)
. Classify each of the following statements as either true or false. If a statement is false, explain why.
If
f
has exactly two critical values at
x
=
a
and
x
=
b
, where
a
<
b
, then there must exist exactly one point of inflection at
x
=
c
such that
a
<
c
<
b
. In other words, exactly one point of inflection must exist between any two critical points.
In Exercises 27–28, let f and g be defined by the following table:
f(x)
g(x)
-2
-1
3
4
-1
1
1
-4
-3
-6
27. Find Vf(-1) – f(0) – [g(2)]² + f(-2) ÷ g(2) ·g(-1).
28. Find |f(1) – f0)| – [g(1)] + g(1) ÷ f(-1)· g(2).
Please explain as detail as possible, thanks.
In Exercises 6–10, let f(x) = cos x, g(x) = Vx+ 2, and
h(x) = 3x?. Write the given function as a composite of two or more
of f, g, and h. For example, cos 3x? is f(h(x)).
6. V cos x + 2
1. V3 cos?x + 2
8. 3 cos x + 6
). cos 27x*
10. cos V2 + 3x²,
Chapter 3 Solutions
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