What is the tangent of f(x)=(x^2)/(x+2),\at x=3 ?

The tangent of f(x)=(x^2)/(x+2),\at x=3 is y= 21/25 x-18/25

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tangent of f(x)=(x^2)/(x+2),\at x=3

tangent of

f (x) = \frac{x ^{2}}{x + 2}, at x = 3

y = \frac{21}{25} x - \frac{18}{25}

Solution steps

Find the tangent point:

(3, \frac{9}{5})

Find the slope of

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

Compute the slope of

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

x = 3 : m = \frac{21}{25}

Find the line with slope m=

\frac{21}{25}

and passing through

(3, \frac{9}{5}) : y = \frac{21}{25} x - \frac{18}{25}

y = \frac{21}{25} x - \frac{18}{25}

\int (6 x^{6} - 2)^{2} (36 x) d x

\int x^{3} x^{2} + 6 d x

\frac{d y}{d x} = \frac{2 x - 1}{y ^{2}}

\frac{\partial}{\partial x} (x y (1 - 7 x - 6 y))

- \frac{( x ^{2} )}{y ^{2}}

What is the tangent of f(x)=(x^2)/(x+2),\at x=3 ?
The tangent of f(x)=(x^2)/(x+2),\at x=3 is y= 21/25 x-18/25