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

The tangent of f(x)=(3x)/(x-2),\at a=4 is y=-6/((a-2)^2)x+(3a^2)/((a-2)^2)

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tangent of f(x)=(3x)/(x-2),\at a=4

tangent of

f (x) = \frac{3 x}{x - 2}, at a = 4

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

Solution steps

Compute the tangent line to the general point

x = a

Find the tangent point:

(a, \frac{3 a}{a - 2})

Find the slope of

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

Compute the slope of

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

x = a : m = - \frac{6}{( a - 2 ) ^{2}}

Find the line with slope m=

- \frac{6}{( a - 2 ) ^{2}}

and passing through

(a, \frac{3 a}{a - 2}) : y = - \frac{6}{( a - 2 ) ^{2}} x + \frac{3 a ^{2}}{( a - 2 ) ^{2}}

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

x \to 4 lim (x - 2)

2 cos (x) + cos^{2} (x)

\int \frac{sin ^{2} ( x )}{1 + cos ( x )} d x

x \to - 2 - lim (\frac{1}{x + 2})

\int 3^{x} - sec^{2} (x) d x

What is the tangent of f(x)=(3x)/(x-2),\at a=4 ?
The tangent of f(x)=(3x)/(x-2),\at a=4 is y=-6/((a-2)^2)x+(3a^2)/((a-2)^2)