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

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

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

tangent of

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

y = - \frac{1}{2} x + \frac{3}{2}

Solution steps

Find the tangent point:

(1, 1)

Find the slope of

f (x) = \frac{2 x}{3 x - 1} : \frac{df ( x )}{d x} = - \frac{2}{( 3 x - 1 ) ^{2}}

Compute the slope of

f (x) = \frac{2 x}{3 x - 1}

x = 1 : m = - \frac{1}{2}

Find the line with slope m=

- \frac{1}{2}

and passing through

(1, 1) : y = - \frac{1}{2} x + \frac{3}{2}

y = - \frac{1}{2} x + \frac{3}{2}

y = - 4

(- 2, 3), (10, 3)

x^{2} - 3 x + 4

f (x) = \frac{x}{x ^{2} + 1}

(4, \frac{π}{2})

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