What is the tangent of f(x)= 3/(2x+1),\at x=4 ?

The tangent of f(x)= 3/(2x+1),\at x=4 is y=-2/27 x+17/27

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tangent of f(x)= 3/(2x+1),\at x=4

tangent of

f (x) = \frac{3}{2 x + 1}, at x = 4

y = - \frac{2}{27} x + \frac{17}{27}

Solution steps

Find the tangent point:

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

Find the slope of

f (x) = \frac{3}{2 x + 1} : \frac{df ( x )}{d x} = - \frac{6}{( 2 x + 1 ) ^{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}{27}

Find the line with slope m=

- \frac{2}{27}

and passing through

(4, \frac{1}{3}) : y = - \frac{2}{27} x + \frac{17}{27}

y = - \frac{2}{27} x + \frac{17}{27}

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What is the tangent of f(x)= 3/(2x+1),\at x=4 ?
The tangent of f(x)= 3/(2x+1),\at x=4 is y=-2/27 x+17/27