What is the tangent of f(x)=(2x+3)/(3x-2) ?

The tangent of f(x)=(2x+3)/(3x-2) is y=-(13)/((3a_{0)-2)^2}x+(6a_{0}^2+18a_{0}-6)/((3a_{0)-2)^2}

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tangent of f(x)=(2x+3)/(3x-2)

tangent of

f (x) = \frac{2 x + 3}{3 x - 2}

y = - \frac{13}{( 3 a _{0} - 2 ) ^{2}} x + \frac{6 a _{0}^{2} + 18 a _{0} - 6}{( 3 a _{0} - 2 ) ^{2}}

Solution steps

Compute the tangent line to the general point

x = a_{0}

Find the tangent point:

(a_{0}, \frac{2 a _{0} + 3}{3 a _{0} - 2})

Find the slope of

f (x) = \frac{2 x + 3}{3 x - 2} : \frac{df ( x )}{d x} = - \frac{13}{( 3 x - 2 ) ^{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{13}{( 3 a _{0} - 2 ) ^{2}}

Find the line with slope m=

- \frac{13}{( 3 a _{0} - 2 ) ^{2}}

and passing through

(a_{0}, \frac{2 a _{0} + 3}{3 a _{0} - 2}) : y = - \frac{13}{( 3 a _{0} - 2 ) ^{2}} x + \frac{6 a _{0}^{2} + 18 a _{0} - 6}{( 3 a _{0} - 2 ) ^{2}}

y = - \frac{13}{( 3 a _{0} - 2 ) ^{2}} x + \frac{6 a _{0}^{2} + 18 a _{0} - 6}{( 3 a _{0} - 2 ) ^{2}}

What is the tangent of f(x)=(2x+3)/(3x-2) ?
The tangent of f(x)=(2x+3)/(3x-2) is y=-(13)/((3a_{0)-2)^2}x+(6a_{0}^2+18a_{0}-6)/((3a_{0)-2)^2}