What is the tangent of f(x)=(64x)/(x^2+64),\at x=-4 ?

The tangent of f(x)=(64x)/(x^2+64),\at x=-4 is y= 12/25 x-32/25

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tangent of f(x)=(64x)/(x^2+64),\at x=-4

tangent of

f (x) = \frac{64 x}{x ^{2} + 64}, at x = - 4

y = \frac{12}{25} x - \frac{32}{25}

Solution steps

Find the tangent point:

(- 4, - \frac{16}{5})

Find the slope of

f (x) = \frac{64 x}{x ^{2} + 64} : \frac{df ( x )}{d x} = \frac{64 ( - x ^{2} + 64 )}{( x ^{2} + 64 ) ^{2}}

Compute the slope of

f (x) = \frac{64 x}{x ^{2} + 64}

x = - 4 : m = \frac{12}{25}

Find the line with slope m=

\frac{12}{25}

and passing through

(- 4, - \frac{16}{5}) : y = \frac{12}{25} x - \frac{32}{25}

y = \frac{12}{25} x - \frac{32}{25}

x \to 0 + lim (sin (x) n x)

f (x) = x^{2} - 4 x + 3, (1, 0)

\int_{0}^{π} sin (x^{2}) d x

\int cot^{3} (x) d x

f (x) = x + 8, (8, 4)

What is the tangent of f(x)=(64x)/(x^2+64),\at x=-4 ?
The tangent of f(x)=(64x)/(x^2+64),\at x=-4 is y= 12/25 x-32/25