Find out the answer to "How do you find the equation of the..."

Efrain Watkins

Answered question

2022-04-15

How do you find the equation of the tangent line when x = 1, include the derivative of

y = \arctan (\sqrt{x})

folytonr4qx

Beginner2022-04-16Added 14 answers

As the curve is

y = \tan^{- 1} (\sqrt{x})

\tan y = \sqrt{x}

and when

x = 1, y = \frac{π}{4}

, so we are seeking a tangent at

(1, \frac{π}{4})

slope of tangent is given by

\frac{d y}{d x}

\tan y = \sqrt{x}

, we have

\sec^{2} y \frac{d y}{d x} = \frac{1}{2 \sqrt{x}}

and

\frac{d y}{d x} = \frac{\cos^{2} y}{2 \sqrt{x}}

and slope of tangent is

\frac{1}{2} \times \frac{1}{2} = \frac{1}{4}

Hence equation of tangent is

y - \frac{π}{4} = \frac{1}{4} (x - 1)

x - 4 y - 1 + π = 0

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