An inflection point is an x-value on the graph where there may be changes in concavity (from concave up to concave down or vice versa). At an inflection point, there isn't necessarily a change in the slope of the graph.
Think of driving on a road with smooth curves. At an inflection point, you may not feel any change in the steering wheel's direction, but you notice that the road starts curving differently.
Concave Up: Concave up refers to the shape of a graph where it curves upward, resembling a smiley face.
Concave Down: Concave down refers to the shape of a graph where it curves downward, resembling a frowning face.
Second Derivative Test: The second derivative test is used to determine whether a critical point on a graph corresponds to a local maximum or minimum by examining the sign of the second derivative.
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