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

The tangent of f(x)= 5/x ,\at x=-1/5 is y=-125x-50

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tangent of f(x)= 5/x ,\at x=-1/5

tangent of

f (x) = \frac{5}{x}, at x = - \frac{1}{5}

y = - 125 x - 50

Solution steps

Find the tangent point:

(- \frac{1}{5}, - 25)

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 = - \frac{1}{5} : m = - 125

Find the line with slope m=

- 125

and passing through

(- \frac{1}{5}, - 25) : y = - 125 x - 50

y = - 125 x - 50

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What is the tangent of f(x)= 5/x ,\at x=-1/5 ?
The tangent of f(x)= 5/x ,\at x=-1/5 is y=-125x-50