Questions: Consider the function graphed at right. The function has a Select an answer of at x= The function is increasing on the interval(s): The function is decreasing on the interval(s):

Consider the function graphed at right. The function has a Select an answer of at x= The function is increasing on the interval(s): The function is decreasing on the interval(s):

Transcript text: Consider the function graphed at right. The function has a Select an answer of $\square$ at $x=$ $\square$ The function is increasing on the interval(s): $\square$ The function is decreasing on the interval(s): $\square$

Solution

Solution Steps

Step 1: Identify the Type of Critical Point

The function has a maximum at $ x = 2 $. This is because the graph reaches its highest point at $ x = 2 $.

Step 2: Determine the Intervals of Increase

The function is increasing on the interval $(- \infty, 2)$. This is because the graph is rising as it approaches $ x = 2 $ from the left.

Step 3: Determine the Intervals of Decrease

The function is decreasing on the interval $(2, \infty)$. This is because the graph is falling as it moves away from $ x = 2 $ to the right.

Final Answer

The function has a maximum at $ x = 2 $.
The function is increasing on the interval $(- \infty, 2)$.
The function is decreasing on the interval $(2, \infty)$.

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