What is the tangent of f(x)=(sqrt(x))/(x+6),\at x=4 ?

The tangent of f(x)=(sqrt(x))/(x+6),\at x=4 is y= 1/200 x+9/50

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tangent of f(x)=(sqrt(x))/(x+6),\at x=4

tangent of

f (x) = \frac{x}{x + 6}, at x = 4

y = \frac{1}{200} x + \frac{9}{50}

Solution steps

Find the tangent point:

(4, \frac{1}{5})

Find the slope of

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

Compute the slope of

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

x = 4 : m = \frac{1}{200}

Find the line with slope m=

\frac{1}{200}

and passing through

(4, \frac{1}{5}) : y = \frac{1}{200} x + \frac{9}{50}

y = \frac{1}{200} x + \frac{9}{50}

e^{\frac{z}{z - 6}}

\int \frac{16 s - 4}{3 - 2 s + 4 s ^{2}} d s

y = tan (e^{3 t}) + e^{t a n (3 t)}

f (x) = e^{r} + r^{e}

\int \frac{3 x}{x ^{2}} d x

What is the tangent of f(x)=(sqrt(x))/(x+6),\at x=4 ?
The tangent of f(x)=(sqrt(x))/(x+6),\at x=4 is y= 1/200 x+9/50