What is the tangent of (x+7)/(x+1) ?

The tangent of (x+7)/(x+1) is y=-6/((a_{0)+1)^2}x+(a_{0}^2+14a_{0}+7)/((a_{0)+1)^2}

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tangent of (x+7)/(x+1)

tangent of

\frac{x + 7}{x + 1}

y = - \frac{6}{( a _{0} + 1 ) ^{2}} x + \frac{a _{0}^{2} + 14 a _{0} + 7}{( a _{0} + 1 ) ^{2}}

Solution steps

Compute the tangent line to the general point

x = a_{0}

Find the tangent point:

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

Find the slope of

y = \frac{x + 7}{x + 1} : \frac{d y}{d x} = - \frac{6}{( x + 1 ) ^{2}}

Compute the slope of

y = \frac{x + 7}{x + 1}

x = a_{0} : m = - \frac{6}{( a _{0} + 1 ) ^{2}}

Find the line with slope m=

- \frac{6}{( a _{0} + 1 ) ^{2}}

and passing through

(a_{0}, \frac{a _{0} + 7}{a _{0} + 1}) : y = - \frac{6}{( a _{0} + 1 ) ^{2}} x + \frac{a _{0}^{2} + 14 a _{0} + 7}{( a _{0} + 1 ) ^{2}}

y = - \frac{6}{( a _{0} + 1 ) ^{2}} x + \frac{a _{0}^{2} + 14 a _{0} + 7}{( a _{0} + 1 ) ^{2}}

y = 4 x^{3} - 4 x, (1, 0)

\int (x + 5) (x^{3} + 5 x - 10) d x

\int - x^{2} ln (x) d x

\int 24 x^{- 3} d x

\int_{0}^{\frac{π}{2}} 8 cos^{5} (x) d x

What is the tangent of (x+7)/(x+1) ?
The tangent of (x+7)/(x+1) is y=-6/((a_{0)+1)^2}x+(a_{0}^2+14a_{0}+7)/((a_{0)+1)^2}