A tangent line is a straight line that touches a curve at only one point without crossing through it. In calculus, we use tangent lines to approximate curves and find instantaneous rates of change.
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The derivative gives us the slope (rate of change) of a function at any given point on its graph. It helps us find tangent lines and analyze functions' behavior.
Concavity describes whether a curve bends upward (concave up) or downward (concave down). We determine concavity by analyzing the second derivative of a function.