For the following exercises, determine intervals where f is increasing or decreasing, local minima and maxima of f , intervals where f is concave up and concave down, and the inflection points of f. Sketch the curve, then use a calculator to compare your answer. If you cannot determine the exact answer analytically, use a calculator. 236. [T] f ( x ) = sin x x over x = [ − 2 π , 2 π ] [ 2 π , 0 ) ∪ ( 0 , 2 π ]
For the following exercises, determine intervals where f is increasing or decreasing, local minima and maxima of f , intervals where f is concave up and concave down, and the inflection points of f. Sketch the curve, then use a calculator to compare your answer. If you cannot determine the exact answer analytically, use a calculator. 236. [T] f ( x ) = sin x x over x = [ − 2 π , 2 π ] [ 2 π , 0 ) ∪ ( 0 , 2 π ]
intervals where f is concave up and concave down, and
the inflection points of f. Sketch the curve, then use a calculator to compare your answer. If you cannot determine the exact answer analytically, use a calculator.
236. [T]
f
(
x
)
=
sin
x
x
over
x
=
[
−
2
π
,
2
π
]
[
2
π
,
0
)
∪
(
0
,
2
π
]
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 .
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