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

The tangent of f(x)= 1/(x+1),\at x=4 is y=-1/25 x+9/25

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

tangent of

f (x) = \frac{1}{x + 1}, at x = 4

y = - \frac{1}{25} x + \frac{9}{25}

Solution steps

Find the tangent point:

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

Find the slope of

f (x) = \frac{1}{x + 1} : \frac{df ( x )}{d x} = - \frac{1}{( x + 1 ) ^{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}{25}

Find the line with slope m=

- \frac{1}{25}

and passing through

(4, \frac{1}{5}) : y = - \frac{1}{25} x + \frac{9}{25}

y = - \frac{1}{25} x + \frac{9}{25}

\int \frac{1}{( x ^{2} - 4 )} d x

\frac{d}{d x} ((2 x)^{6 x})

\frac{d}{d x} ((x^{5} - 4 x^{3} - 7)^{8})

\frac{d}{d x} (\frac{0.07 e ^{x}}{sin ( x )})

y = (x - 2)^{x + 1}

What is the tangent of f(x)= 1/(x+1),\at x=4 ?
The tangent of f(x)= 1/(x+1),\at x=4 is y=-1/25 x+9/25