What is the tangent of f(x)=((x-5))/((x-6),(7,2)) ?

The tangent of f(x)=((x-5))/((x-6),(7,2)) is

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tangent of f(x)=((x-5))/((x-6),(7,2))

tangent of

f (x) = \frac{( x - 5 )}{( x - 6 ) , ( 7 , 2 )}

y = \frac{1}{, ( 7 , 2 )} \cdot \frac{1 \cdot ( a _{0} - 6 ) - 1 \cdot ( a _{0} - 5 )}{( a _{0} - 6 ) ^{2}} x + \frac{a _{0} - 5}{( a _{0} - 6 ) , ( 7 , 2 )} - \frac{1}{, ( 7 , 2 )} \cdot \frac{1 \cdot ( a _{0} - 6 ) - 1 \cdot ( a _{0} - 5 )}{( a _{0} - 6 ) ^{2}} a_{0}

Solution steps

Compute the tangent line to the general point

x = a_{0}

Find the tangent point:

(a_{0}, \frac{a _{0} - 5}{( a _{0} - 6 ) , ( 7 , 2 )})

Find the slope of

f (x) = \frac{x - 5}{( x - 6 ) , ( 7 , 2 )} : \frac{df ( x )}{d x} = \frac{1}{, ( 7 , 2 )} \cdot \frac{1 \cdot ( x - 6 ) - 1 \cdot ( x - 5 )}{( x - 6 ) ^{2}}

Compute the slope of

f (x) = \frac{x - 5}{( x - 6 ) , ( 7 , 2 )}

x = a_{0} : m = \frac{1}{, ( 7 , 2 )} \cdot \frac{1 \cdot ( a _{0} - 6 ) - 1 \cdot ( a _{0} - 5 )}{( a _{0} - 6 ) ^{2}}

Find the line with slope m=

\frac{1}{, ( 7 , 2 )} \frac{1 ( a _{0} - 6 ) - 1 ( a _{0} - 5 )}{( a _{0} - 6 ) ^{2}}

and passing through

(a_{0}, \frac{a _{0} - 5}{( a _{0} - 6 ) , ( 7 , 2 )}) : y = \frac{1}{, ( 7 , 2 )} \cdot \frac{1 \cdot ( a _{0} - 6 ) - 1 \cdot ( a _{0} - 5 )}{( a _{0} - 6 ) ^{2}} x + \frac{a _{0} - 5}{( a _{0} - 6 ) , ( 7 , 2 )} - \frac{1}{, ( 7 , 2 )} \cdot \frac{1 \cdot ( a _{0} - 6 ) - 1 \cdot ( a _{0} - 5 )}{( a _{0} - 6 ) ^{2}} a_{0}

y = \frac{1}{, ( 7 , 2 )} \cdot \frac{1 \cdot ( a _{0} - 6 ) - 1 \cdot ( a _{0} - 5 )}{( a _{0} - 6 ) ^{2}} x + \frac{a _{0} - 5}{( a _{0} - 6 ) , ( 7 , 2 )} - \frac{1}{, ( 7 , 2 )} \cdot \frac{1 \cdot ( a _{0} - 6 ) - 1 \cdot ( a _{0} - 5 )}{( a _{0} - 6 ) ^{2}} a_{0}

\frac{d}{d x} (12 x^{3} - 12 x^{2} - 24 x)

sin (1 + cos (x))

\int 20 e^{- 20 x} d x

\int_{3}^{\infty} x e^{- 3 x} d x

f (x) = x

What is the tangent of f(x)=((x-5))/((x-6),(7,2)) ?
The tangent of f(x)=((x-5))/((x-6),(7,2)) is