What is the tangent of f(x)=-1/((x-5)^2),\at x=-4 ?

The tangent of f(x)=-1/((x-5)^2),\at x=-4 is y=-2/729 x-17/729

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tangent of f(x)=-1/((x-5)^2),\at x=-4

tangent of

f (x) = - \frac{1}{( x - 5 ) ^{2}}, at x = - 4

y = - \frac{2}{729} x - \frac{17}{729}

Solution steps

Find the tangent point:

(- 4, - \frac{1}{81})

Find the slope of

f (x) = - \frac{1}{( x - 5 ) ^{2}} : \frac{df ( x )}{d x} = \frac{2}{( x - 5 ) ^{3}}

Compute the slope of

f (x) = - \frac{1}{( x - 5 ) ^{2}}

x = - 4 : m = - \frac{2}{729}

Find the line with slope m=

- \frac{2}{729}

and passing through

(- 4, - \frac{1}{81}) : y = - \frac{2}{729} x - \frac{17}{729}

y = - \frac{2}{729} x - \frac{17}{729}

\int \frac{x ^{3} + 3 x - 1}{x ^{4} - 4 x ^{2}} d x

x \to 0 - lim (\frac{e ^{3 x}}{2 x})

\frac{d y}{d x} = x y^{4} - y

x \to 1 - f lim (x)

\frac{d}{d x} ((1 + 8 x^{2}) (x - x^{2}))

What is the tangent of f(x)=-1/((x-5)^2),\at x=-4 ?
The tangent of f(x)=-1/((x-5)^2),\at x=-4 is y=-2/729 x-17/729