What is the tangent of f(x)= 1/x ,\at x=3 ?

The tangent of f(x)= 1/x ,\at x=3 is y=-1/9 x+2/3

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tangent of f(x)= 1/x ,\at x=3

tangent of

f (x) = \frac{1}{x}, at x = 3

y = - \frac{1}{9} x + \frac{2}{3}

Solution steps

Find the tangent point:

(3, \frac{1}{3})

Find the slope of

f (x) = \frac{1}{x} : \frac{df ( x )}{d x} = - \frac{1}{x ^{2}}

Compute the slope of

f (x) = \frac{1}{x}

x = 3 : m = - \frac{1}{9}

Find the line with slope m=

- \frac{1}{9}

and passing through

(3, \frac{1}{3}) : y = - \frac{1}{9} x + \frac{2}{3}

y = - \frac{1}{9} x + \frac{2}{3}

x \to + 0 lim ((1 + 6 x)^{\frac{4}{x}})

\frac{d}{d x} (- 2 e^{x} sin (x))

\int x e^{4 x^{2}} d x

x \to 5 + lim (\frac{x + 5}{x + 5})

\int x^{- 2} + x^{- 1} + 1 + x + cos (x) d x

What is the tangent of f(x)= 1/x ,\at x=3 ?
The tangent of f(x)= 1/x ,\at x=3 is y=-1/9 x+2/3