What is the tangent of f(x)= 4/x ,\at x=-9 ?

The tangent of f(x)= 4/x ,\at x=-9 is y=-4/81 x-8/9

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tangent of f(x)= 4/x ,\at x=-9

tangent of

f (x) = \frac{4}{x}, at x = - 9

y = - \frac{4}{81} x - \frac{8}{9}

Solution steps

Find the tangent point:

(- 9, - \frac{4}{9})

Find the slope of

f (x) = \frac{4}{x} : \frac{df ( x )}{d x} = - \frac{4}{x ^{2}}

EN : T i tl e G e n er a l Eq u a t i o n Sl o p e A t P o in t 2 Eq : m = - \frac{4}{81}

Find the line with slope m=

- \frac{4}{81}

and passing through

(- 9, - \frac{4}{9}) : y = - \frac{4}{81} x - \frac{8}{9}

y = - \frac{4}{81} x - \frac{8}{9}

What is the tangent of f(x)= 4/x ,\at x=-9 ?
The tangent of f(x)= 4/x ,\at x=-9 is y=-4/81 x-8/9