What is the tangent of f(x)=(-2x)/((x^2+1)),\at x=-1 ?

The tangent of f(x)=(-2x)/((x^2+1)),\at x=-1 is y=1

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tangent of f(x)=(-2x)/((x^2+1)),\at x=-1

tangent of

f (x) = \frac{- 2 x}{( x ^{2} + 1 )}, at x = - 1

y = 1

Solution steps

Find the tangent point:

(- 1, 1)

Find the slope of

f (x) = \frac{- 2 x}{x ^{2} + 1} : \frac{df ( x )}{d x} = - \frac{2 ( - x ^{2} + 1 )}{( x ^{2} + 1 ) ^{2}}

Compute the slope of

f (x) = \frac{- 2 x}{x ^{2} + 1}

x = - 1 : m = 0

Find the line with slope m=

0

and passing through

(- 1, 1) : y = 1

y = 1

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What is the tangent of f(x)=(-2x)/((x^2+1)),\at x=-1 ?
The tangent of f(x)=(-2x)/((x^2+1)),\at x=-1 is y=1