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

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

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tangent of 2/(x-4)

tangent of

\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_{0}^{3} 1

\frac{\partial}{\partial z} (x)

\int_{0}^{\frac{4}{3}} \frac{1}{16 + 9 x ^{2}} d x

\int sin (9 x) cos (4 x) d x

\int_{1}^{2} I n x d x

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