What is the tangent of f(x)= x/(-6x+6),\at x=2 ?

The tangent of f(x)= x/(-6x+6),\at x=2 is y= 1/6 x-2/3

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tangent of f(x)= x/(-6x+6),\at x=2

tangent of

f (x) = \frac{x}{- 6 x + 6}, at x = 2

y = \frac{1}{6} x - \frac{2}{3}

Solution steps

Find the tangent point:

(2, - \frac{1}{3})

Find the slope of

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

Compute the slope of

f (x) = \frac{x}{- 6 x + 6}

x = 2 : m = \frac{1}{6}

Find the line with slope m=

\frac{1}{6}

and passing through

(2, - \frac{1}{3}) : y = \frac{1}{6} x - \frac{2}{3}

y = \frac{1}{6} x - \frac{2}{3}

\frac{d}{d x} (\frac{x ^{2} - 3 x + 1}{x})

x \to 5 lim (\frac{1}{( x - 5 ) ^{2}})

\int \frac{x ^{2}}{2 1 - x ^{2}} d x

\frac{d}{d x} (\frac{x}{2 π})

\int \frac{( x ^{2} )}{5 + 2 x ^{3}} d x

What is the tangent of f(x)= x/(-6x+6),\at x=2 ?
The tangent of f(x)= x/(-6x+6),\at x=2 is y= 1/6 x-2/3