What is the tangent of f(x)= 4/(x+1),\at x=6 ?

The tangent of f(x)= 4/(x+1),\at x=6 is y=-4/49 x+52/49

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tangent of f(x)= 4/(x+1),\at x=6

tangent of

f (x) = \frac{4}{x + 1}, at x = 6

y = - \frac{4}{49} x + \frac{52}{49}

Solution steps

Find the tangent point:

(6, \frac{4}{7})

Find the slope of

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

Compute the slope of

f (x) = \frac{4}{x + 1}

x = 6 : m = - \frac{4}{49}

Find the line with slope m=

- \frac{4}{49}

and passing through

(6, \frac{4}{7}) : y = - \frac{4}{49} x + \frac{52}{49}

y = - \frac{4}{49} x + \frac{52}{49}

\int \frac{1}{2 y - 1} d y

y = (x^{3} + 2) (3 x^{2} - 4 x + 2), (1, 3)

x^{2} (2.4)

\int 7 x + 5 d x

\int \frac{( 2 + x )}{1 - x ^{2}} d x

What is the tangent of f(x)= 4/(x+1),\at x=6 ?
The tangent of f(x)= 4/(x+1),\at x=6 is y=-4/49 x+52/49