Consider the function below. f(x) = 4 + 2x2 − x4 (a) Find the interval of increase. (Enter your answer using interval notation.)     Find the interval of decrease. (Enter your answer using interval notation.)     (b) Find the local minimum value(s). (Enter your answers as a comma-separated list. If an answer does not exist, enter DNE.)     Find the local maximum value(s). (Enter your answers as a comma-separated list. If an answer does not exist, enter DNE.)     (c) Find the inflection points. (x, y)  =           (smaller x-value) (x, y)  =           (larger x-value) Find the interval where the graph is concave upward. (Enter your answer using interval notation.)     Find the interval where the graph is concave downward. (Enter your answer using interval notation.)

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter3: Functions And Graphs
Section3.5: Graphs Of Functions
Problem 36E
Question

Consider the function below.

f(x) = 4 + 2x2 − x4
(a) Find the interval of increase. (Enter your answer using interval notation.)
 
 


Find the interval of decrease. (Enter your answer using interval notation.)
 
 


(b) Find the local minimum value(s). (Enter your answers as a comma-separated list. If an answer does not exist, enter DNE.)
 
 


Find the local maximum value(s). (Enter your answers as a comma-separated list. If an answer does not exist, enter DNE.)
 
 


(c) Find the inflection points.
(x, y)  = 
 
 
 
 
 (smaller x-value)
(x, y)  = 
 
 
 
 
 (larger x-value)


Find the interval where the graph is concave upward. (Enter your answer using interval notation.)
 
 


Find the interval where the graph is concave downward. (Enter your answer using interval notation.)
 
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