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

The tangent of f(x)=(2x^2)/((1-2x)4),\at x=2 is y=-2/9 x-2/9

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

tangent of

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

y = - \frac{2}{9} x - \frac{2}{9}

Solution steps

Find the tangent point:

(2, - \frac{2}{3})

Find the slope of

f (x) = \frac{2 x ^{2}}{( 1 - 2 x ) 4} : \frac{df ( x )}{d x} = \frac{x ( - x + 1 )}{( 1 - 2 x ) ^{2}}

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{2}{9}

Find the line with slope m=

- \frac{2}{9}

and passing through

(2, - \frac{2}{3}) : y = - \frac{2}{9} x - \frac{2}{9}

y = - \frac{2}{9} x - \frac{2}{9}

x \to - \infty lim (3 x)

\int x sin (- x) d x

\frac{s + 1}{s ^{2} + s - 1}

x \to 0 lim (\frac{1}{2} + e^{\frac{1}{x}})

\frac{d}{d x} (x (x - 2)^{\frac{2}{3}})

What is the tangent of f(x)=(2x^2)/((1-2x)4),\at x=2 ?
The tangent of f(x)=(2x^2)/((1-2x)4),\at x=2 is y=-2/9 x-2/9