Find an equation of the tangent line to the curve at the...

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Key Concepts

Tangent Line

A tangent line to a curve at a given point is a straight line that touches the curve at that point without crossing it locally. This line represents the instantaneous direction of the curve and has the same slope as the curve at the point of tangency.

Derivative

The derivative of a function at a particular point provides the slope of the tangent line to the curve at that point. It is a fundamental tool in calculus for determining rates of change and is computed using the rules of differentiation.

Differentiation

Differentiation is the process of finding the derivative of a function. It involves applying rules such as the power rule, product rule, and chain rule to compute the instantaneous rate of change of the function with respect to its variable.

Point-Slope Form

The point-slope form of a linear equation is used to write the equation of a line when the slope and a point on the line are known. It is expressed as y - y? = m(x - x?), where m is the slope and (x?, y?) is the given point.

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