Is it true that the function has no inflection points? Verify this by using the Second Derivative Test.

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Calculus 1

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Determine when functions are increasing or decreasing, concavity, and inflection

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JanineLv8

30 Aug 2020

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For the following function , find the inflection points, and use the second derivative test, if possible, to classify the critical points. In addition, sketch the graph of the function.

For the function, , what are the inflection points? How do you use the second derivative test, if possible, to classify the critical points? How do you sketch the graph of the function?

3. (a) Assume that a function f(x) is concave down on its whole domain, and f(0) = -2 and f'(0) = -1. Circle each statement that must be true: • The function f(2) has no inflection points. • The derivative f'(2) is always negative. • The derivative satisfies f'(3) < -1. • The derivative satisfies f'(-3) < -1. • The function f(x) <-2 for all 1 >0. (b) Sketch a graph of a function f() satisfying all of the following conditions: • The derivative function f'(x) is decreasing when x < 1 and when r > 3. • The derivative function f'(2) is increasing when 1

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