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

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

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

tangent of

\frac{x ^{2}}{x + 4}

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

Solution steps

Compute the tangent line to the general point

x = a_{0}

Find the tangent point:

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

Find the slope of

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

Find the line with slope m=

\frac{a _{0}^{2} + 8 a _{0}}{( a _{0} + 4 ) ^{2}}

and passing through

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

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

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