What is the tangent of f(x)=(13x-1)^{-1/3},\at x=5 ?

The tangent of f(x)=(13x-1)^{-1/3},\at x=5 is y=-13/768 x+257/768

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tangent of f(x)=(13x-1)^{-1/3},\at x=5

tangent of

f (x) = (13 x - 1)^{- \frac{1}{3}}, at x = 5

y = - \frac{13}{768} x + \frac{257}{768}

Solution steps

Find the tangent point:

(5, \frac{1}{4})

Find the slope of

f (x) = (13 x - 1)^{- \frac{1}{3}} : \frac{df ( x )}{d x} = - \frac{13}{3 ( 13 x - 1 ) ^{\frac{4}{3}}}

Compute the slope of

f (x) = (13 x - 1)^{- \frac{1}{3}}

x = 5 : m = - \frac{13}{768}

Find the line with slope m=

- \frac{13}{768}

and passing through

(5, \frac{1}{4}) : y = - \frac{13}{768} x + \frac{257}{768}

y = - \frac{13}{768} x + \frac{257}{768}

\frac{t}{( t - 9 ) ^{2}}

25 y^{^{''}} + 30 y^{^{'}} + 9 y = 0

\frac{\partial}{\partial x} (2 x^{0.3} y^{0.3} + 1)

\int \frac{3 x ^{\frac{8}{3}}}{8} + C d x

\int arccot (5 x) d x

What is the tangent of f(x)=(13x-1)^{-1/3},\at x=5 ?
The tangent of f(x)=(13x-1)^{-1/3},\at x=5 is y=-13/768 x+257/768