What is the tangent of f(x)=(x-3)/(6x-1),\at x=1 ?

The tangent of f(x)=(x-3)/(6x-1),\at x=1 is y= 17/25 x-27/25

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tangent of f(x)=(x-3)/(6x-1),\at x=1

tangent of

f (x) = \frac{x - 3}{6 x - 1}, at x = 1

y = \frac{17}{25} x - \frac{27}{25}

Solution steps

Find the tangent point:

(1, - \frac{2}{5})

Find the slope of

f (x) = \frac{x - 3}{6 x - 1} : \frac{df ( x )}{d x} = \frac{17}{( 6 x - 1 ) ^{2}}

Compute the slope of

f (x) = \frac{x - 3}{6 x - 1}

x = 1 : m = \frac{17}{25}

Find the line with slope m=

\frac{17}{25}

and passing through

(1, - \frac{2}{5}) : y = \frac{17}{25} x - \frac{27}{25}

y = \frac{17}{25} x - \frac{27}{25}

y^{^{''}} + 4 y^{^{'}} + 4 y = 12 t e^{- 2 t} + 4 t

(x + 2)^{2} + (y - 3)^{2} = 37, (- 1, 9)

\int tan (4 x) sec^{2} (4 x) d x

x^{2} - e^{y^{2}}

y = arctan (e^{x})

What is the tangent of f(x)=(x-3)/(6x-1),\at x=1 ?
The tangent of f(x)=(x-3)/(6x-1),\at x=1 is y= 17/25 x-27/25