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13 Nov 2019

Find the intervals of concavity and inflection points, if any, of functions f(x) = 9cos2(x) - 18sin(x) [0, 2π] and f(x) = ln( 7 - ln(x) )

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Beverley Smith
Beverley SmithLv2
13 May 2019

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Related questions

Concavity Interval and Inflection Points


Problem 1.

Consider the function f(x) = sin x cos x + 5 on the interval (0, 2π ).

a) Find the open interval(s) on which the function is increasing or decreasing.

b) Apply the First Derivative Test to identify all relative extrema.

Problem 2.

Find the points of inflection and discuss the concavity of the graph of the function.

f(x) = (x - 2)3 (x - 1)

Problem 3.

Find the points of inflection and discuss the concavity of the graph of the function.

f(x) = 2 sin x + cos 2x on [0, 2π ]

Problem 4.

Analyze and sketch a graph of the function. Label any intercepts, relative extrema, points of inflection, and asymptotes.

g(x) = x √(9 - x2)

Consider the function f(x) = sin x cos x + 5 on the interval (0, 2π ).

a) Find the open interval(s) on which the function is increasing or decreasing.

b) Apply the First Derivative Test to identify all relative extrema.

Problem 2.

Find the points of inflection and discuss the concavity of the graph of the function.

f(x) = (x - 2)3 (x - 1)

Problem 3.

Find the points of inflection and discuss the concavity of the graph of the function.

f(x) = 2 sin x + cos 2x on [0, 2π ]

Problem 4.

Analyze and sketch a graph of the function. Label any intercepts, relative extrema, points of inflection, and asymptotes.

g(x) = x √(9 - x2)

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