What is the tangent of 1/(x+4),\at x=5 ?

The tangent of 1/(x+4),\at x=5 is y=-1/81 x+14/81

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tangent of 1/(x+4),\at x=5

tangent of

\frac{1}{x + 4}, at x = 5

y = - \frac{1}{81} x + \frac{14}{81}

Solution steps

Find the tangent point:

(5, \frac{1}{9})

Find the slope of

y = \frac{1}{x + 4} : \frac{d y}{d x} = - \frac{1}{( x + 4 ) ^{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}{81}

Find the line with slope m=

- \frac{1}{81}

and passing through

(5, \frac{1}{9}) : y = - \frac{1}{81} x + \frac{14}{81}

y = - \frac{1}{81} x + \frac{14}{81}

ln (x^{3} + 2 x^{2} + 2 x)

\int \frac{4 x}{x - 1} d x

y^{^{''}} - y = 0, y (0) = 1, y^{^{'}} (0) = 0

y^{^{'}} = 5 t y^{2}

9 x^{- 2}

What is the tangent of 1/(x+4),\at x=5 ?
The tangent of 1/(x+4),\at x=5 is y=-1/81 x+14/81