What is the tangent of f(x)= 2/x ,\at x=5 ?

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

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tangent of f(x)= 2/x ,\at x=5

tangent of

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

Compute the slope of

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

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}

e^{3 x}

\int \frac{x + 5}{x + 6} d x

\frac{d}{d x} (cos (x) - sin (x))

\frac{d y}{d x} = x^{9} + 1

t^{2} \frac{d y}{d t} + 4 t y - y^{3} = 0, y (1) = \frac{3}{2}

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