What is the tangent of y= 2/(x-4) ?

The tangent of y= 2/(x-4) is y=-2/((a_{0)-4)^2}x+(4a_{0}-8)/((a_{0)-4)^2}

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tangent of y= 2/(x-4)

tangent of

y = \frac{2}{x - 4}

y = - \frac{2}{( a _{0} - 4 ) ^{2}} x + \frac{4 a _{0} - 8}{( a _{0} - 4 ) ^{2}}

Solution steps

Compute the tangent line to the general point

x = a_{0}

Find the tangent point:

(a_{0}, \frac{2}{a _{0} - 4})

Find the slope of

y = \frac{2}{x - 4} : \frac{d y}{d x} = - \frac{2}{( x - 4 ) ^{2}}

Compute the slope of

y = \frac{2}{x - 4}

x = a_{0} : m = - \frac{2}{( a _{0} - 4 ) ^{2}}

Find the line with slope m=

- \frac{2}{( a _{0} - 4 ) ^{2}}

and passing through

(a_{0}, \frac{2}{a _{0} - 4}) : y = - \frac{2}{( a _{0} - 4 ) ^{2}} x + \frac{4 a _{0} - 8}{( a _{0} - 4 ) ^{2}}

y = - \frac{2}{( a _{0} - 4 ) ^{2}} x + \frac{4 a _{0} - 8}{( a _{0} - 4 ) ^{2}}

\int \frac{1}{k - x} d x

\int \frac{x + 21}{x ^{2} + 28 x + 200} d x

\int 4^{x} + ln (5^{x}) d x

\frac{3}{s ^{2} + 7}

What is the tangent of y= 2/(x-4) ?
The tangent of y= 2/(x-4) is y=-2/((a_{0)-4)^2}x+(4a_{0}-8)/((a_{0)-4)^2}