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

The tangent of f(x)= 1/(3+2x),\at x=2 is y=-2/49 x+11/49

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

tangent of

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

y = - \frac{2}{49} x + \frac{11}{49}

Solution steps

Find the tangent point:

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

Find the slope of

f (x) = \frac{1}{3 + 2 x} : \frac{df ( x )}{d x} = - \frac{2}{( 3 + 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}{49}

Find the line with slope m=

- \frac{2}{49}

and passing through

(2, \frac{1}{7}) : y = - \frac{2}{49} x + \frac{11}{49}

y = - \frac{2}{49} x + \frac{11}{49}

What is the tangent of f(x)= 1/(3+2x),\at x=2 ?
The tangent of f(x)= 1/(3+2x),\at x=2 is y=-2/49 x+11/49