What is the tangent of f(x)=(sqrt(x))/(x+5),\at x=4 ?

The tangent of f(x)=(sqrt(x))/(x+5),\at x=4 is y= 1/324 x+17/81

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tangent of f(x)=(sqrt(x))/(x+5),\at x=4

tangent of

f (x) = \frac{x}{x + 5}, at x = 4

y = \frac{1}{324} x + \frac{17}{81}

Solution steps

Find the tangent point:

(4, \frac{2}{9})

Find the slope of

f (x) = \frac{x}{x + 5} : \frac{df ( x )}{d x} = \frac{- x + 5}{2 x ( x + 5 ) ^{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{1}{324}

Find the line with slope m=

\frac{1}{324}

and passing through

(4, \frac{2}{9}) : y = \frac{1}{324} x + \frac{17}{81}

y = \frac{1}{324} x + \frac{17}{81}

(3, 5), (- 1, 5)

\int_{0}^{4} x x d x

\frac{d}{d x} (4 e^{x} sin (x))

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

\int x^{2} \cdot ln (2 x) d x

What is the tangent of f(x)=(sqrt(x))/(x+5),\at x=4 ?
The tangent of f(x)=(sqrt(x))/(x+5),\at x=4 is y= 1/324 x+17/81