What is the tangent of f(x)=(-2)/(2x-14) ?

The tangent of f(x)=(-2)/(2x-14) is y= 1/((a_{0)-7)^2}x+(-2a_{0}+7)/((a_{0)-7)^2}

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tangent of f(x)=(-2)/(2x-14)

tangent of

f (x) = \frac{- 2}{2 x - 14}

y = \frac{1}{( a _{0} - 7 ) ^{2}} x + \frac{- 2 a _{0} + 7}{( a _{0} - 7 ) ^{2}}

Solution steps

Compute the tangent line to the general point

x = a_{0}

Find the tangent point:

(a_{0}, - \frac{1}{a _{0} - 7})

Find the slope of

f (x) = \frac{- 2}{2 x - 14} : \frac{df ( x )}{d x} = \frac{1}{( x - 7 ) ^{2}}

EN : T i tl e G e n er a l Eq u a t i o n Sl o p e A t P o in t 2 Eq : m = \frac{1}{( a _{0} - 7 ) ^{2}}

Find the line with slope m=

\frac{1}{( a _{0} - 7 ) ^{2}}

and passing through

(a_{0}, - \frac{1}{a _{0} - 7}) : y = \frac{1}{( a _{0} - 7 ) ^{2}} x + \frac{- 2 a _{0} + 7}{( a _{0} - 7 ) ^{2}}

y = \frac{1}{( a _{0} - 7 ) ^{2}} x + \frac{- 2 a _{0} + 7}{( a _{0} - 7 ) ^{2}}

x \to 1 - lim (\frac{1}{ln ( x )})

y = 9 - 6 x, at x = - 1

\int \frac{x ^{6}}{( x - 2 ) ^{2} ( 1 - x ) ^{5}} d x

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

x \to 4 - lim (\frac{- 1}{x - 4})

What is the tangent of f(x)=(-2)/(2x-14) ?
The tangent of f(x)=(-2)/(2x-14) is y= 1/((a_{0)-7)^2}x+(-2a_{0}+7)/((a_{0)-7)^2}