Use the given graph of f over the interval (0, 7) to find the following. The ope

Question

Use the given graph of f over the interval (0, 7) to find the following. The open intervals on which f is increasing. (Enter your answer using interval notation.) The open intervals on which f is decreasing. (Enter your answer using interval notation.) The open intervals on which f is concave upward. (Enter your answer using interval notation.) The open intervals on which f is concave downward. (Enter your answer using interval notation.) The coordinates of the points of inflection, (x, y) = () (smallest x-value) (x, y) = () (x, y) = () (largest x-value)

Explanation / Answer

a) Increasing :
Just by looking, we can say that increasing over
(0 , 1) U (3 , 5) U (5 , 7) ---> ANSWER

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b) Decreasing :
(1 , 3) ---> ANSWER

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c) Concave up :
Where does the graph look like an upward facing U?
This happens over (2 , 4) and (5 , 7)
So, (2 , 4) U (5 , 7) ----> ANSWER

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d) Concave down :
Where does the graph look like a downward facing U?
This is over (0 , 2) U (4 , 5) ---> ANSWER

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e) Pts of inflection :
(2 , 2) --> smallest
(4 , 3.75)
(5 , 4) ---> largest

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