What is the tangent of f(x)= 1/(5+2x),(2, 1/9) ?

The tangent of f(x)= 1/(5+2x),(2, 1/9) is y=-2/81 x+13/81

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tangent of f(x)= 1/(5+2x),(2, 1/9)

tangent of

f (x) = \frac{1}{5 + 2 x}, (2, \frac{1}{9})

y = - \frac{2}{81} x + \frac{13}{81}

Solution steps

Find the slope of

f (x) = \frac{1}{5 + 2 x} : \frac{df ( x )}{d x} = - \frac{2}{( 5 + 2 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}{81}

Find the line with slope m=

- \frac{2}{81}

and passing through

(2, \frac{1}{9}) : y = - \frac{2}{81} x + \frac{13}{81}

y = - \frac{2}{81} x + \frac{13}{81}

What is the tangent of f(x)= 1/(5+2x),(2, 1/9) ?
The tangent of f(x)= 1/(5+2x),(2, 1/9) is y=-2/81 x+13/81