What is the tangent of f(x)= 2/x ,(-6,-1/3) ?

The tangent of f(x)= 2/x ,(-6,-1/3) is y=-1/18 x-2/3

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tangent of f(x)= 2/x ,(-6,-1/3)

tangent of

f (x) = \frac{2}{x}, (- 6, - \frac{1}{3})

y = - \frac{1}{18} x - \frac{2}{3}

Solution steps

Find the slope of

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

Compute the slope of

f (x) = \frac{2}{x}

(- 6, - \frac{1}{3}) : m = - \frac{1}{18}

Find the line with slope m=

- \frac{1}{18}

and passing through

(- 6, - \frac{1}{3}) : y = - \frac{1}{18} x - \frac{2}{3}

y = - \frac{1}{18} x - \frac{2}{3}

\frac{d y}{d x} = 4 y^{3}

(2 x y + y) d x + (x^{2} - x) d y = 0

\frac{d y}{d x} - \frac{y}{x} = x^{2}

x \to 0 + lim (12 cos (12 x))

x y^{^{'}} + 2 y = sin (x), y (π) = \frac{1}{π}

What is the tangent of f(x)= 2/x ,(-6,-1/3) ?
The tangent of f(x)= 2/x ,(-6,-1/3) is y=-1/18 x-2/3