True/False: Determine whether each of the statements that follow is true or false. If a statement is true, explain why. If a statement is false, provide a counterexample.

(a) True or False: If, thenis an inflection point of.

(b) True or False: Ifis concave up on an interval I, then it is positive on I.

(c) True or False: Ifis concave up on an interval I, thenis positive on I.

(d) True or False: Ifdoes not exist andis in the domain of, thenis a critical point of the function.

(e) True or False: Ifhas an inflection point atandis differentiable at, then the derivativehas a local minimum or maximum at.

(f) True or False: Ifand, thenhas a local minimum at.

(g) True or False: The second-derivative test involves checking the sign of the second derivative on each side of every critical point.

(h) True or False: The second-derivative test always produces exactly the same information as the first-derivative test.

Step by step solution

01

a

a

02

a

a

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