Question

the graph of (y = f(x)) is shown below. assume the domain of (f(x)) and (f(x)) are both ((-\infty, \infty)).

remember this is the graph of (y = f(x)), not the graph of (y = f(x))

based on this graph:

(y = f(x)) is increasing on the interval(s)

(y = f(x)) is decreasing on the interval(s)

therefore (f(x)) has a max at (x =) and a local min at (x =)

(y = f(x)) is concave up on the interval(s)

(y = f(x)) is concave down on the interval(s)

therefore (f(x)) has inflection point(s) at (x =)

Explanation:

Determine increasing and decreasing intervals

Using the Increasing and Decreasing Intervals and Interval Notation knowledge points

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Identify local extrema

Using the Critical Points and Local Extrema knowledge points

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Determine concavity intervals

Using the Concavity and Interval Notation knowledge points

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Identify inflection points

Using the Inflection Points knowledge point

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Answer:

Based on this graph:

\(y = f(x)\) is increasing on the interval(s) <blank>\((-\infty, -1) \cup (1, \infty)\)</blank>

\(y = f(x)\) is decreasing on the interval(s) <blank>\((-1, 1)\)</blank>

Therefore \(f(x)\) has a max at \(x =\) <blank>\(-1\)</blank> and a local min at \(x =\) <blank>\(1\)</blank>

\(y = f(x)\) is concave up on the interval(s) <blank>\((0, \infty)\)</blank>

\(y = f(x)\) is concave down on the interval(s) <blank>\((-\infty, 0)\)</blank>

Therefore \(f(x)\) has inflection point(s) at \(x =\) <blank>\(0\)</blank>