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

The tangent of f(x)= x/(1+x^2),\at x=2 is y=-3/25 x+16/25

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

tangent

y = - \frac{3}{25} x + \frac{16}{25}

Solution steps

Find the tangent point:

(2, \frac{2}{5})

Find the slope of

f (x) = \frac{x}{1 + x ^{2}} : \frac{df ( x )}{d x} = \frac{1 - x ^{2}}{( 1 + x ^{2} ) ^{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{3}{25}

Find the line with slope m=

- \frac{3}{25}

and passing through

(2, \frac{2}{5}) : y = - \frac{3}{25} x + \frac{16}{25}

y = - \frac{3}{25} x + \frac{16}{25}

What is the tangent of f(x)= x/(1+x^2),\at x=2 ?
The tangent of f(x)= x/(1+x^2),\at x=2 is y=-3/25 x+16/25