What is the tangent of f(x)=(4x^2)/(x+2) ?

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

tangent of f(x)=(4x^2)/(x+2)

tangent of

f (x) = \frac{4 x ^{2}}{x + 2}

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

Solution steps

Compute the tangent line to the general point

x = a_{0}

Find the tangent point:

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

Find the slope of

f (x) = \frac{4 x ^{2}}{x + 2} : \frac{df ( x )}{d x} = \frac{4 ( x ^{2} + 4 x )}{( x + 2 ) ^{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{4 ( a _{0}^{2} + 4 a _{0} )}{( a _{0} + 2 ) ^{2}}

Find the line with slope m=

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

and passing through

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

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

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