A smooth, planar curve refers to a curved line that does not have any sharp corners or cusps. It is continuous and can be represented by an equation.
Imagine drawing a perfect circle using only one stroke without lifting your pen. The resulting shape would be a smooth, planar curve.
Derivative: The rate at which a function changes with respect to its independent variable. It represents the slope of a tangent line to a curve.
Concavity: Describes whether a graph is bending upward or downward over an interval.
Inflection Point: A point on a graph where concavity changes from positive to negative (or vice versa), indicating where it switches from bending upward to downward (or vice versa).
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