What is the tangent of f(x)=2x^{-1},\at x=5 ?

The tangent of f(x)=2x^{-1},\at x=5 is y=-2/25 x+4/5

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tangent of f(x)=2x^{-1},\at x=5

tangent of

f (x) = 2 x^{- 1}, at x = 5

y = - \frac{2}{25} x + \frac{4}{5}

Solution steps

Find the tangent point:

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

Find the slope of

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

Compute the slope of

f (x) = 2 x^{- 1}

x = 5 : m = - \frac{2}{25}

Find the line with slope m=

- \frac{2}{25}

and passing through

(5, \frac{2}{5}) : y = - \frac{2}{25} x + \frac{4}{5}

y = - \frac{2}{25} x + \frac{4}{5}

\int_{\frac{1}{2}}^{\frac{3}{2}} (- 2 x + 4) d x

\int (2 x - 5) e^{x^{2} - 5 x} d x

\frac{d y}{d x} + 2 x y = 0

\int_{- 3}^{0} (2 + 9 - x^{2}) d x

n = 0 \sum \infty n e^{- 2 n}

What is the tangent of f(x)=2x^{-1},\at x=5 ?
The tangent of f(x)=2x^{-1},\at x=5 is y=-2/25 x+4/5