a. Find the open intervals on which the function is increasing and those on which it is decreasing. b. Identify the function's local extreme values, if any, saying where they occur. 16. f(x) 3x In x a. On what open intervals, if any, is the function increasing? Select the correct choice below and, if necessary, fill in the answer box to complete your choice. O A. The function f is increasing on the open interval(s) (Type your answer in interval notation. Type exact answers. Use a comma to separate answers as needed.) B. The function is never increasing On what open intervals, if any, is the function decreasing? Select the correct choice below and, if necessary, fill in the answer box to complete your choice. O A. The function f is decreasing on the open interval(s) (Type your answer in interval notation. Type exact answers. Use a comma to separate answers as needed.) O B. The function is never decreasing b. Find each local maximum, if any. Select the correct choice below and, if necessary, fill in the answer boxes to complete your choice. (Type exact answers.) O A. The function has a local maximum value at two values of x. In increasing order of x-value, the maximum values are f and f O B. The function has a local maximum value at one value of x. The maximum value is f O C. The function has a local maximum value at three values of x. In increasing order of x-value, the maximum values are f( and = O D. There are no local maxima. Find each local minimum, if any. Select the correct choice below and, if necessary, fill in the answer boxes to complete your choice (Type exact answers.) O A. The function has a local minimum value at three values of x. In increasing order of x-value, the minimum values are f and O B. The function has a local minimum value at one value of x. The minimum value is f( O C. The function has a local minimum value at two values of x. In increasing order of x-value, the minimum values are f and f O D. There are no local minima. II
a. Find the open intervals on which the function is increasing and those on which it is decreasing. b. Identify the function's local extreme values, if any, saying where they occur. 16. f(x) 3x In x a. On what open intervals, if any, is the function increasing? Select the correct choice below and, if necessary, fill in the answer box to complete your choice. O A. The function f is increasing on the open interval(s) (Type your answer in interval notation. Type exact answers. Use a comma to separate answers as needed.) B. The function is never increasing On what open intervals, if any, is the function decreasing? Select the correct choice below and, if necessary, fill in the answer box to complete your choice. O A. The function f is decreasing on the open interval(s) (Type your answer in interval notation. Type exact answers. Use a comma to separate answers as needed.) O B. The function is never decreasing b. Find each local maximum, if any. Select the correct choice below and, if necessary, fill in the answer boxes to complete your choice. (Type exact answers.) O A. The function has a local maximum value at two values of x. In increasing order of x-value, the maximum values are f and f O B. The function has a local maximum value at one value of x. The maximum value is f O C. The function has a local maximum value at three values of x. In increasing order of x-value, the maximum values are f( and = O D. There are no local maxima. Find each local minimum, if any. Select the correct choice below and, if necessary, fill in the answer boxes to complete your choice (Type exact answers.) O A. The function has a local minimum value at three values of x. In increasing order of x-value, the minimum values are f and O B. The function has a local minimum value at one value of x. The minimum value is f( O C. The function has a local minimum value at two values of x. In increasing order of x-value, the minimum values are f and f O D. There are no local minima. II
College Algebra (MindTap Course List)
12th Edition
ISBN:9781305652231
Author:R. David Gustafson, Jeff Hughes
Publisher:R. David Gustafson, Jeff Hughes
Chapter3: Functions
Section3.3: More On Functions; Piecewise-defined Functions
Problem 98E: Determine if the statemment is true or false. If the statement is false, then correct it and make it...
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Transcribed Image Text:a. Find the open intervals on which the function is increasing and those on which it is decreasing.
b. Identify the function's local extreme values, if any, saying where they occur.
16.
f(x) 3x In x
a. On what open intervals, if any, is the function increasing? Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
O A. The function f is increasing on the open interval(s)
(Type your answer in interval notation. Type exact answers. Use a comma to separate answers as needed.)
B. The function is never increasing
On what open intervals, if any, is the function decreasing? Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
O A. The function f is decreasing on the open interval(s)
(Type your answer in interval notation. Type exact answers. Use a comma to separate answers as needed.)
O B. The function is never decreasing
b. Find each local maximum, if any. Select the correct choice below and, if necessary, fill in the answer boxes to complete your choice.
(Type exact answers.)
O A. The function has a local maximum value at two values of x. In increasing order of x-value, the maximum values are f
and f
O B. The function has a local maximum value at one value of x. The maximum value is f
O C. The function has a local maximum value at three values of x. In increasing order of x-value, the maximum values are f(
and
=
O D. There are no local maxima.
Find each local minimum, if any. Select the correct choice below and, if necessary, fill in the answer boxes to complete your choice
(Type exact answers.)
O A. The function has a local minimum value at three values of x. In increasing order of x-value, the minimum values are f
and
O B. The function has a local minimum value at one value of x. The minimum value is f(
O C. The function has a local minimum value at two values of x. In increasing order of x-value, the minimum values are f
and f
O D. There are no local minima.
II
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