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

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

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

tangent of

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

y = \frac{6}{49} x + \frac{1}{49}

Solution steps

Find the tangent point:

(1, \frac{1}{7})

Find the slope of

f (x) = \frac{x}{x + 6} : \frac{df ( x )}{d x} = \frac{6}{( x + 6 ) ^{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{6}{49}

Find the line with slope m=

\frac{6}{49}

and passing through

(1, \frac{1}{7}) : y = \frac{6}{49} x + \frac{1}{49}

y = \frac{6}{49} x + \frac{1}{49}

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