What is the tangent of f(x)=(2x-1)/(x+5),\at x=4 ?

The tangent of f(x)=(2x-1)/(x+5),\at x=4 is y= 11/81 x+19/81

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tangent of f(x)=(2x-1)/(x+5),\at x=4

tangent of

f (x) = \frac{2 x - 1}{x + 5}, at x = 4

y = \frac{11}{81} x + \frac{19}{81}

Solution steps

Find the tangent point:

(4, \frac{7}{9})

Find the slope of

f (x) = \frac{2 x - 1}{x + 5} : \frac{df ( x )}{d x} = \frac{11}{( x + 5 ) ^{2}}

Compute the slope of

f (x) = \frac{2 x - 1}{x + 5}

x = 4 : m = \frac{11}{81}

Find the line with slope m=

\frac{11}{81}

and passing through

(4, \frac{7}{9}) : y = \frac{11}{81} x + \frac{19}{81}

y = \frac{11}{81} x + \frac{19}{81}

\int \frac{x ^{2} + 9}{x ^{4}} d x

sin (5 x)

d p = (3 p - p^{2} - \frac{9}{4}) d t

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

\int \frac{e ^{\frac{5}{t}}}{t ^{2}} d t

What is the tangent of f(x)=(2x-1)/(x+5),\at x=4 ?
The tangent of f(x)=(2x-1)/(x+5),\at x=4 is y= 11/81 x+19/81