What is the tangent of sqrt(x-2) ?

The tangent of sqrt(x-2) is y= 1/(2sqrt(a_{0)-2)}x+sqrt(a_{0)-2}-(a_{0})/(2sqrt(a_{0)-2)}

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tangent of sqrt(x-2)

tangent of

x - 2

y = \frac{1}{2 a _{0} - 2} x + a_{0} - 2 - \frac{a _{0}}{2 a _{0} - 2}

Solution steps

Compute the tangent line to the general point

x = a_{0}

Find the tangent point:

(a_{0}, a_{0} - 2)

Find the slope of

y = x - 2 : \frac{d y}{d x} = \frac{1}{2 x - 2}

EN : T i tl e G e n er a l Eq u a t i o n Sl o p e A t P o in t 2 Eq : m = \frac{1}{2 a _{0} - 2}

Find the line with slope m=

\frac{1}{2 a _{0} - 2}

and passing through

(a_{0}, a_{0} - 2) : y = \frac{1}{2 a _{0} - 2} x + a_{0} - 2 - \frac{a _{0}}{2 a _{0} - 2}

y = \frac{1}{2 a _{0} - 2} x + a_{0} - 2 - \frac{a _{0}}{2 a _{0} - 2}

What is the tangent of sqrt(x-2) ?
The tangent of sqrt(x-2) is y= 1/(2sqrt(a_{0)-2)}x+sqrt(a_{0)-2}-(a_{0})/(2sqrt(a_{0)-2)}