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

The tangent of f(x)=(x^2)/(x+4),\at x=2 is y= 5/9 x-4/9

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

tangent of

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

y = \frac{5}{9} x - \frac{4}{9}

Solution steps

Find the tangent point:

(2, \frac{2}{3})

Find the slope of

f (x) = \frac{x ^{2}}{x + 4} : \frac{df ( x )}{d x} = \frac{x ^{2} + 8 x}{( x + 4 ) ^{2}}

Compute the slope of

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

x = 2 : m = \frac{5}{9}

Find the line with slope m=

\frac{5}{9}

and passing through

(2, \frac{2}{3}) : y = \frac{5}{9} x - \frac{4}{9}

y = \frac{5}{9} x - \frac{4}{9}

\frac{d y}{d x} - 2 y = 4 - x

x \to \infty lim (\frac{4 x ^{- 1} - 2 x ^{- 3}}{3 x ^{- 2} + x ^{- 5}})

e^{- \frac{t}{2}} - \frac{e ^{- \frac{t}{2}} t}{2}

y = 8 x - 6, (64, 58)

\int_{7}^{9} (x^{2} + 2 x - 5) d x

What is the tangent of f(x)=(x^2)/(x+4),\at x=2 ?
The tangent of f(x)=(x^2)/(x+4),\at x=2 is y= 5/9 x-4/9