What is the tangent of f(x)=(2x-1)/(x+9),\at x=1 ?

The tangent of f(x)=(2x-1)/(x+9),\at x=1 is y= 19/100 x-9/100

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tangent of f(x)=(2x-1)/(x+9),\at x=1

tangent of

f (x) = \frac{2 x - 1}{x + 9}, at x = 1

y = \frac{19}{100} x - \frac{9}{100}

Solution steps

Find the tangent point:

(1, \frac{1}{10})

Find the slope of

f (x) = \frac{2 x - 1}{x + 9} : \frac{df ( x )}{d x} = \frac{19}{( x + 9 ) ^{2}}

Compute the slope of

f (x) = \frac{2 x - 1}{x + 9}

x = 1 : m = \frac{19}{100}

Find the line with slope m=

\frac{19}{100}

and passing through

(1, \frac{1}{10}) : y = \frac{19}{100} x - \frac{9}{100}

y = \frac{19}{100} x - \frac{9}{100}

f (x) = \frac{( 4 - 2 x ) ^{5}}{x ^{3} + 12}

x \to \infty lim (x^{2} - 3)

y^{^{''}} - 2 y + 6 = 0

\frac{\partial}{\partial x} (e^{- 6 y} sin (6 x))

What is the tangent of f(x)=(2x-1)/(x+9),\at x=1 ?
The tangent of f(x)=(2x-1)/(x+9),\at x=1 is y= 19/100 x-9/100