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

The tangent of f(x)= 5/x ,\at x=5 is y=-1/5 x+2

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

tangent of

f (x) = \frac{5}{x}, at x = 5

y = - \frac{1}{5} x + 2

Solution steps

Find the tangent point:

(5, 1)

Find the slope of

f (x) = \frac{5}{x} : \frac{df ( x )}{d x} = - \frac{5}{x ^{2}}

Compute the slope of

f (x) = \frac{5}{x}

x = 5 : m = - \frac{1}{5}

Find the line with slope m=

- \frac{1}{5}

and passing through

(5, 1) : y = - \frac{1}{5} x + 2

y = - \frac{1}{5} x + 2

\int \frac{3 x}{x + 1} d x

\int 64 cos^{4} (8 x) d x

\int 4 e^{2 t} d t

10 y^{^{''}} + 60 y^{^{'}} + 50 y = 0

\frac{d}{d x} (e^{\frac{- x}{3}})

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