What is the tangent of (6x)/(x+8),\at x=1 ?

The tangent of (6x)/(x+8),\at x=1 is y= 16/27 x+2/27

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tangent of (6x)/(x+8),\at x=1

tangent of

\frac{6 x}{x + 8}, at x = 1

y = \frac{16}{27} x + \frac{2}{27}

Solution steps

Find the tangent point:

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

Find the slope of

y = \frac{6 x}{x + 8} : \frac{d y}{d x} = \frac{48}{( x + 8 ) ^{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{16}{27}

Find the line with slope m=

\frac{16}{27}

and passing through

(1, \frac{2}{3}) : y = \frac{16}{27} x + \frac{2}{27}

y = \frac{16}{27} x + \frac{2}{27}

What is the tangent of (6x)/(x+8),\at x=1 ?
The tangent of (6x)/(x+8),\at x=1 is y= 16/27 x+2/27