What is the tangent of f(x)=(x^2)/(x+6) ?

The tangent of f(x)=(x^2)/(x+6) is y=(a_{0}^2+12a_{0})/((a_{0)+6)^2}x-(6a_{0}^2)/((a_{0)+6)^2}

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tangent of f(x)=(x^2)/(x+6)

tangent of

f (x) = \frac{x ^{2}}{x + 6}

y = \frac{a _{0}^{2} + 12 a _{0}}{( a _{0} + 6 ) ^{2}} x - \frac{6 a _{0}^{2}}{( a _{0} + 6 ) ^{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} + 6})

Find the slope of

f (x) = \frac{x ^{2}}{x + 6} : \frac{df ( x )}{d x} = \frac{x ^{2} + 12 x}{( x + 6 ) ^{2}}

Compute the slope of

f (x) = \frac{x ^{2}}{x + 6}

x = a_{0} : m = \frac{a _{0}^{2} + 12 a _{0}}{( a _{0} + 6 ) ^{2}}

Find the line with slope m=

\frac{a _{0}^{2} + 12 a _{0}}{( a _{0} + 6 ) ^{2}}

and passing through

(a_{0}, \frac{a _{0}^{2}}{a _{0} + 6}) : y = \frac{a _{0}^{2} + 12 a _{0}}{( a _{0} + 6 ) ^{2}} x - \frac{6 a _{0}^{2}}{( a _{0} + 6 ) ^{2}}

y = \frac{a _{0}^{2} + 12 a _{0}}{( a _{0} + 6 ) ^{2}} x - \frac{6 a _{0}^{2}}{( a _{0} + 6 ) ^{2}}

x \to - \infty lim (2^{x} + 3)

y^{^{''}} - y^{^{'}} + \frac{1}{4} y = 5 + e^{\frac{x}{2}}

x^{2} (1 - 8 x)

\frac{d N}{d t} + N = Nt e^{t + 8}

\frac{d}{d x} (\frac{1 + x ^{3}}{1 - x ^{3}})

What is the tangent of f(x)=(x^2)/(x+6) ?
The tangent of f(x)=(x^2)/(x+6) is y=(a_{0}^2+12a_{0})/((a_{0)+6)^2}x-(6a_{0}^2)/((a_{0)+6)^2}