What is the tangent of f(x)= 2/(4-x),\at x=1 ?

The tangent of f(x)= 2/(4-x),\at x=1 is y= 2/9 x+4/9

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tangent of f(x)= 2/(4-x),\at x=1

tangent of

f (x) = \frac{2}{4 - x}, at x = 1

y = \frac{2}{9} x + \frac{4}{9}

Solution steps

Find the tangent point:

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

Find the slope of

f (x) = \frac{2}{4 - x} : \frac{df ( x )}{d x} = \frac{2}{( 4 - x ) ^{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{2}{9}

Find the line with slope m=

\frac{2}{9}

and passing through

(1, \frac{2}{3}) : y = \frac{2}{9} x + \frac{4}{9}

y = \frac{2}{9} x + \frac{4}{9}

What is the tangent of f(x)= 2/(4-x),\at x=1 ?
The tangent of f(x)= 2/(4-x),\at x=1 is y= 2/9 x+4/9