`f(x) = sqrt(x), (1, 1)` 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 29 - 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^(1/2) 

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

f'(x) = (1/2)*[1/{x^(1/2)}]

Now, slope of the tangent at the point (1,1) = f'(1) = 1/2

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

y - 1 = (1/2)*(x - 1)

or, 2y - 2 = x - 1

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

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