What is the tangent of f(x)= 1/(x^4),\at x=3 ?

The tangent of f(x)= 1/(x^4),\at x=3 is y=-4/243 x+5/81

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tangent of f(x)= 1/(x^4),\at x=3

tangent of

f (x) = \frac{1}{x ^{4}}, at x = 3

y = - \frac{4}{243} x + \frac{5}{81}

Solution steps

Find the tangent point:

(3, \frac{1}{81})

Find the slope of

f (x) = \frac{1}{x ^{4}} : \frac{df ( x )}{d x} = - \frac{4}{x ^{5}}

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}{243}

Find the line with slope m=

- \frac{4}{243}

and passing through

(3, \frac{1}{81}) : y = - \frac{4}{243} x + \frac{5}{81}

y = - \frac{4}{243} x + \frac{5}{81}

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\int x^{2} + 3 x - 1000000 d x

\frac{1}{x + 9}

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\int 7 x^{3} + 4 x^{2} d x

What is the tangent of f(x)= 1/(x^4),\at x=3 ?
The tangent of f(x)= 1/(x^4),\at x=3 is y=-4/243 x+5/81