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Let f(x) = x² − 1. Find the equation of the tangent line to the graph of f at the point x0 = 2.

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Answer to a math question Let f(x) = x² − 1. Find the equation of the tangent line to the graph of f at the point x0 = 2.

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Darrell
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Solution: Find the point in the function at x=2 by substitution f(2)=2^2−1 f(2)=3 Find the slope of the tangent line of the function, which is given by the first derivative of the function, at x=2 f^{\prime}(x)=2x f^{\prime}(2)=2\cdot2 f^{\prime}(2)=4 Using the point-slope form of a linear equation to formulate the equation of the tangent line, y-y_0=m\left(x-x_0\right) y-3=4\left(x-2\right) y-3=4x-8 y=4x-5 Answer: y=4x-5

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