What is the tangent of 6x^{-3},\at x=5 ?

The tangent of 6x^{-3},\at x=5 is y=-18/625 x+24/125

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tangent of 6x^{-3},\at x=5

tangent of

6 x^{- 3}, at x = 5

y = - \frac{18}{625} x + \frac{24}{125}

Solution steps

Find the tangent point:

(5, \frac{6}{125})

Find the slope of

y = 6 x^{- 3} : \frac{d y}{d x} = - \frac{18}{x ^{4}}

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{18}{625}

Find the line with slope m=

- \frac{18}{625}

and passing through

(5, \frac{6}{125}) : y = - \frac{18}{625} x + \frac{24}{125}

y = - \frac{18}{625} x + \frac{24}{125}

What is the tangent of 6x^{-3},\at x=5 ?
The tangent of 6x^{-3},\at x=5 is y=-18/625 x+24/125