Find the intervals on which the graph of f is concave​ upward, the intervals on which the graph of f is concave​ downward, and the inflection points.

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter3: Functions And Graphs
Section3.5: Graphs Of Functions
Problem 39E
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Find the intervals on which the graph of f is concave​ upward, the intervals on which the graph of f is concave​ downward, and the inflection points.

Find the intervals on which the graph of f is concave upward, the intervals on which the graph of f is concave downward,
and the inflection points.
4
f(x) = − x² + 16x³ – 16x+5
For what interval(s) of x is the graph of f concave upward? Select the correct choice below and, if necessary, fill in the
answer box to complete your choice.
A.
(Type your answer in interval notation. Type an exact answer. Use a comma to separate answers as needed.)
B. The graph is never concave upward.
For what interval(s) of x is the graph of f concave downward? Select the correct choice below and, if necessary, fill in the
answer box to complete your choice.
A.
(Type your answer in interval notation. Type an exact answer. Use a comma to separate answers as needed.)
B. The graph is never concave downward.
Determine the x coordinates of any inflection points of the graph of f(x). Select the correct choice below and, if
necessary, fill in the answer box to complete your choice.
(Type an exact answer. Use a comma to separate answers as needed.)
A. X=
B. There are no inflection points.
Transcribed Image Text:Find the intervals on which the graph of f is concave upward, the intervals on which the graph of f is concave downward, and the inflection points. 4 f(x) = − x² + 16x³ – 16x+5 For what interval(s) of x is the graph of f concave upward? Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. (Type your answer in interval notation. Type an exact answer. Use a comma to separate answers as needed.) B. The graph is never concave upward. For what interval(s) of x is the graph of f concave downward? Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. (Type your answer in interval notation. Type an exact answer. Use a comma to separate answers as needed.) B. The graph is never concave downward. Determine the x coordinates of any inflection points of the graph of f(x). Select the correct choice below and, if necessary, fill in the answer box to complete your choice. (Type an exact answer. Use a comma to separate answers as needed.) A. X= B. There are no inflection points.
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