`f(x) = x^2 + 2x - 1, (1, 2)` Find an equation of the tangent line to the graph of f at the given point.

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Chapter 2, 2.1 - Problem 26 - Calculus of a Single Variable (10th Edition, Ron Larson).
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hkj1385 | (Level 1) Assistant Educator

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The given function is:-

f(x) = (x^2) + 2x

differentiating both sides w.r.t 'x' we get

f'(x) = 2x + 2

Now, slope of the tangent at the point (1,2) = f'(1) = (2*1) + 2 = 4

Thus, equation of the tangent at the point (1,2) and having slope = 4 is :-

y - 2 = 4*(x - 1)

or, y - 2 = 4x - 4

or, y - 4x + 2 = 0 is the equation of the tangent to the  given curve at (1,2)

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