What is the tangent of f(x)= 3/x ,\at x=3 ?

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

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tangent of f(x)= 3/x ,\at x=3

tangent of

f (x) = \frac{3}{x}, at x = 3

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

Solution steps

Find the tangent point:

(3, 1)

Find the slope of

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

Compute the slope of

f (x) = \frac{3}{x}

x = 3 : m = - \frac{1}{3}

Find the line with slope m=

- \frac{1}{3}

and passing through

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

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

\frac{d}{d x} (\frac{3 x - 3}{2 x})

\frac{d y}{d x} = \frac{3}{1 + x}

f (x) = 3 cos (2 x)

\frac{\partial}{\partial x} (sin (x) - cos (y))

\frac{d}{d x} (arctanh (x))

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