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

The tangent of f(x)=(16x)/(x^2+16),\at x=-2 is y= 12/25 x-16/25

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tangent of f(x)=(16x)/(x^2+16),\at x=-2

tangent of

f (x) = \frac{16 x}{x ^{2} + 16}, at x = - 2

y = \frac{12}{25} x - \frac{16}{25}

Solution steps

Find the tangent point:

(- 2, - \frac{8}{5})

Find the slope of

f (x) = \frac{16 x}{x ^{2} + 16} : \frac{df ( x )}{d x} = \frac{16 ( - x ^{2} + 16 )}{( x ^{2} + 16 ) ^{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{12}{25}

Find the line with slope m=

\frac{12}{25}

and passing through

(- 2, - \frac{8}{5}) : y = \frac{12}{25} x - \frac{16}{25}

y = \frac{12}{25} x - \frac{16}{25}

What is the tangent of f(x)=(16x)/(x^2+16),\at x=-2 ?
The tangent of f(x)=(16x)/(x^2+16),\at x=-2 is y= 12/25 x-16/25