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

The tangent of f(x)= 4/(3x-1),\at x=3 is y=-3/16 x+17/16

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

tangent of

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

y = - \frac{3}{16} x + \frac{17}{16}

Solution steps

Find the tangent point:

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

Find the slope of

f (x) = \frac{4}{3 x - 1} : \frac{df ( x )}{d x} = - \frac{12}{( 3 x - 1 ) ^{2}}

Compute the slope of

f (x) = \frac{4}{3 x - 1}

x = 3 : m = - \frac{3}{16}

Find the line with slope m=

- \frac{3}{16}

and passing through

(3, \frac{1}{2}) : y = - \frac{3}{16} x + \frac{17}{16}

y = - \frac{3}{16} x + \frac{17}{16}

ln (4 x^{3} + 5 x^{2} + 2 x + 5)

\int \frac{( x ^{2} - 64 )}{x} d x

\frac{s}{s ^{2} + 6 s + 11}

y = 5 - x^{2}, y = 17 - 7 x

\int \frac{x + 5}{x ^{2} + 16} d x

What is the tangent of f(x)= 4/(3x-1),\at x=3 ?
The tangent of f(x)= 4/(3x-1),\at x=3 is y=-3/16 x+17/16