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

The tangent of f(x)= 1/(x+1),\at x=1 is y=-1/4 x+3/4

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

tangent of

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

y = - \frac{1}{4} x + \frac{3}{4}

Solution steps

Find the tangent point:

(1, \frac{1}{2})

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}{4}

Find the line with slope m=

- \frac{1}{4}

and passing through

(1, \frac{1}{2}) : y = - \frac{1}{4} x + \frac{3}{4}

y = - \frac{1}{4} x + \frac{3}{4}

\frac{d}{d x} (\frac{( x + 1 )}{x ^{2} + x + 1})

\int \frac{7}{x ^{2} ( x ^{2} + 25 )} d x

f (x) = e^{- 2 x^{2}}

\frac{d y}{d x} + 20 = 24

\frac{\partial}{\partial x} (e^{x} + 1)

What is the tangent of f(x)= 1/(x+1),\at x=1 ?
The tangent of f(x)= 1/(x+1),\at x=1 is y=-1/4 x+3/4