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

The tangent of f(x)=(2x-1)/(x+9),\at x=2 is y= 19/121 x-5/121

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

tangent of

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

y = \frac{19}{121} x - \frac{5}{121}

Solution steps

Find the tangent point:

(2, \frac{3}{11})

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 = 2 : m = \frac{19}{121}

Find the line with slope m=

\frac{19}{121}

and passing through

(2, \frac{3}{11}) : y = \frac{19}{121} x - \frac{5}{121}

y = \frac{19}{121} x - \frac{5}{121}

y = arccsc (4 x)

\int tan^{3} (θ) d θ

x y^{^{''}} + 2 y^{^{'}} = 8 x^{2}

\frac{\partial}{\partial y} (x e^{x y^{2}})

What is the tangent of f(x)=(2x-1)/(x+9),\at x=2 ?
The tangent of f(x)=(2x-1)/(x+9),\at x=2 is y= 19/121 x-5/121