What can be inferred about the graph of a function if it has a local maximum?
Practice Questions
Q1
What can be inferred about the graph of a function if it has a local maximum?
The function is increasing at that point.
The function is decreasing at that point.
The derivative at that point is zero.
The function has no other critical points.
Questions & Step-by-Step Solutions
What can be inferred about the graph of a function if it has a local maximum?
Step 1: Understand what a local maximum is. A local maximum is a point on the graph where the function reaches a peak compared to nearby points.
Step 2: Recognize that at a peak, the slope of the graph changes direction. This means the graph goes up before the peak and down after the peak.
Step 3: The slope of the graph is represented by the derivative of the function. When the slope is zero, it means the graph is flat (horizontal) at that point.
Step 4: Therefore, at a local maximum, the derivative of the function is equal to zero, indicating a horizontal tangent line.
