Extrema
Definition
Extrema refers to the highest and lowest points of a function, which can be either maximum or minimum values.
Analogy
Think of extrema as the peaks and valleys on a roller coaster ride. The highest point represents the maximum value, while the lowest point represents the minimum value.
Related terms
X-intercepts: These are the points where a graph intersects the x-axis. They occur when y = 0.
Y-intercepts: These are the points where a graph intersects the y-axis. They occur when x = 0.
Critical Points: These are points on a graph where its derivative is either zero or undefined. They can be potential extrema.
"Extrema" appears in:
Additional resources (1)
Practice Questions (3)
The Second Derivative Test is a valuable tool for determining extrema because it allows us to analyze the concavity of a function at critical points. By examining the sign of the second derivative, we can identify whether a critical point corresponds to a relative minimum, relative maximum, or what else?
When asked where an extrema occurs for a function, what value should one give?
When asked what an extrema for a function is, what value should one give?
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