What is the graph of a function f that satisfies the conditions: f' (x) > 0 on (-∞, –1) U (–1, ∞) f'(-1) = 0 f" (x) > 0 on (–1, 0) f" (x) < 0 on (–∞, –1) (-1,0) is the only inflection point of f(x)

College Algebra
1st Edition
ISBN:9781938168383
Author:Jay Abramson
Publisher:Jay Abramson
Chapter3: Functions
Section3.3: Rates Of Change And Behavior Of Graphs
Problem 2SE: If a functionfis increasing on (a,b) and decreasing on (b,c) , then what can be said about the local...
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this question isn't not complete. I don't understand which graph matches the description given

What is the graph of a function f that satisfies the following
conditions:
· f (x) > 0 on (-∞, –1) U (-1, ∞)
• f'(-1) = 0
f" (x) > 0 on (-1, ∞)
• f'" (x) < 0 on (-∞, –1)
• (-1,0) is the only inflection point of f(x)
Transcribed Image Text:What is the graph of a function f that satisfies the following conditions: · f (x) > 0 on (-∞, –1) U (-1, ∞) • f'(-1) = 0 f" (x) > 0 on (-1, ∞) • f'" (x) < 0 on (-∞, –1) • (-1,0) is the only inflection point of f(x)
Expert Solution
Step 1

f'(x)>0 on (-,-1)  U (-1,)

when second derivative is positive then the function f(x) is increasing

So f(X) is increasing over the given intervals 

In first and second options the graph is increasing

 

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