Q. 12
Question
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 , then
is an inflection point of
.
(b) True or False: If is concave up on an interval I, then it is positive on I.
(c) True or False: If is concave up on an interval I, then
is positive on I.
(d) True or False: If does not exist and
is in the domain of
, then
is a critical point of the function
.
(e) True or False: If has an inflection point at
and
is differentiable at
, then the derivative
has a local minimum or maximum at
.
(f) True or False: If and
, then
has 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
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