What is the tangent of f(x)= x/((3x-2)^4),\at x=1 ?

The tangent of f(x)= x/((3x-2)^4),\at x=1 is y=-11x+12

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tangent of f(x)= x/((3x-2)^4),\at x=1

tangent of

f (x) = \frac{x}{( 3 x - 2 ) ^{4}}, at x = 1

y = - 11 x + 12

Solution steps

Find the tangent point:

(1, 1)

Find the slope of

f (x) = \frac{x}{( 3 x - 2 ) ^{4}} : \frac{df ( x )}{d x} = \frac{- 2 - 9 x}{( 3 x - 2 ) ^{5}}

Compute the slope of

f (x) = \frac{x}{( 3 x - 2 ) ^{4}}

x = 1 : m = - 11

Find the line with slope m=

- 11

and passing through

(1, 1) : y = - 11 x + 12

y = - 11 x + 12

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What is the tangent of f(x)= x/((3x-2)^4),\at x=1 ?
The tangent of f(x)= x/((3x-2)^4),\at x=1 is y=-11x+12