What is the tangent of f(x)= x/(x-3) ?

The tangent of f(x)= x/(x-3) is y=-3/((a_{0)-3)^2}x+(a_{0}^2)/((a_{0)-3)^2}

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

tangent of f(x)= x/(x-3)

tangent of

f (x) = \frac{x}{x - 3}

y = - \frac{3}{( a _{0} - 3 ) ^{2}} x + \frac{a _{0}^{2}}{( a _{0} - 3 ) ^{2}}

Solution steps

Compute the tangent line to the general point

x = a_{0}

Find the tangent point:

(a_{0}, \frac{a _{0}}{a _{0} - 3})

Find the slope of

f (x) = \frac{x}{x - 3} : \frac{df ( x )}{d x} = - \frac{3}{( x - 3 ) ^{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{3}{( a _{0} - 3 ) ^{2}}

Find the line with slope m=

- \frac{3}{( a _{0} - 3 ) ^{2}}

and passing through

(a_{0}, \frac{a _{0}}{a _{0} - 3}) : y = - \frac{3}{( a _{0} - 3 ) ^{2}} x + \frac{a _{0}^{2}}{( a _{0} - 3 ) ^{2}}

y = - \frac{3}{( a _{0} - 3 ) ^{2}} x + \frac{a _{0}^{2}}{( a _{0} - 3 ) ^{2}}

What is the tangent of f(x)= x/(x-3) ?
The tangent of f(x)= x/(x-3) is y=-3/((a_{0)-3)^2}x+(a_{0}^2)/((a_{0)-3)^2}