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

The tangent of f(x)=(2x)/(3-4x^3),\at x= 1/2 is y= 32/25 x-6/25

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

tangent of

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

y = \frac{32}{25} x - \frac{6}{25}

Solution steps

Find the tangent point:

(\frac{1}{2}, \frac{2}{5})

Find the slope of

f (x) = \frac{2 x}{3 - 4 x ^{3}} : \frac{df ( x )}{d x} = \frac{2 ( 3 + 8 x ^{3} )}{( 3 - 4 x ^{3} ) ^{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{32}{25}

Find the line with slope m=

\frac{32}{25}

and passing through

(\frac{1}{2}, \frac{2}{5}) : y = \frac{32}{25} x - \frac{6}{25}

y = \frac{32}{25} x - \frac{6}{25}

What is the tangent of f(x)=(2x)/(3-4x^3),\at x= 1/2 ?
The tangent of f(x)=(2x)/(3-4x^3),\at x= 1/2 is y= 32/25 x-6/25