Find an equation of the tangent line to the graph of the given function at the indicated value o

step 1 All right, so we want to find the tangent line to this function at the value x equals 2. So firs

Find an equation of the tangent line to the graph of the...

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Key Concepts

Evaluation of the Derivative at a Point

To determine the slope of the tangent line at a specific point, the derivative of the function is evaluated at that point. This process involves substituting the x-value of the point into the derivative, which yields the instantaneous rate of change of the function there.

Point-Slope Form

The point-slope form is a method for writing the equation of a line when a point on the line and the slope are known. It is expressed as y - y1 = m(x - x1), where (x1, y1) is the given point and m is the slope. This form is particularly useful for constructing the equation of a tangent line once the slope from the derivative is found.

Derivative

The derivative of a function is a measure of the rate at which the function value changes with respect to a change in its input. It is calculated using limits and provides the slope of the tangent line to the function at any given point. This concept is fundamental in calculus for understanding instantaneous rates of change.

Tangent Line

A tangent line is a straight line that touches the graph of a function at a specific point without crossing it locally. It provides a linear approximation of the function near that point, with its slope determined by the derivative of the function evaluated at that point.

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