Michael J. answered • 03/10/17

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Effective High School STEM Tutor & CUNY Math Peer Leader

The tangent line is finding the derivative, not find the anti-derivative.

Rewrite the equation using rational exponents.

y = x

^{1/2}The equation of the tangent line is

y = (dy/dx)(x - x

_{1}) + y_{1}**where:**

dy/dx is the slope of the tangent line at the target point

(x

_{1 }, y_{1}) is the point that satisfies the functionNow we find the slope of the tangent line. This is the derivative.

dy/dx = (1/2)x

^{-1/2}dy/dx = 1 / (2√x)

dy/dx = 1 / (2√4)

dy/dx = 1 / 4

Tangent line is then

y = (1/4)(x - 4) + 2

**y = (1/4)x + 1**