What is the tangent of f(x)= x/(x^2+9),\at x=0 ?

The tangent of f(x)= x/(x^2+9),\at x=0 is y= 1/9 x

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tangent of f(x)= x/(x^2+9),\at x=0

tangent of

f (x) = \frac{x}{x ^{2} + 9}, at x = 0

y = \frac{1}{9} x

Solution steps

Find the tangent point:

(0, 0)

Find the slope of

f (x) = \frac{x}{x ^{2} + 9} : \frac{df ( x )}{d x} = \frac{- x ^{2} + 9}{( x ^{2} + 9 ) ^{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}{9}

Find the line with slope m=

\frac{1}{9}

and passing through

(0, 0) : y = \frac{1}{9} x

y = \frac{1}{9} x

What is the tangent of f(x)= x/(x^2+9),\at x=0 ?
The tangent of f(x)= x/(x^2+9),\at x=0 is y= 1/9 x