What is the tangent of f(x)=(12x)/(x^2-4),(4,4) ?

The tangent of f(x)=(12x)/(x^2-4),(4,4) is y=-5/3 x+32/3

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tangent of f(x)=(12x)/(x^2-4),(4,4)

tangent of

f (x) = \frac{12 x}{x ^{2} - 4}, (4, 4)

y = - \frac{5}{3} x + \frac{32}{3}

Solution steps

Find the slope of

f (x) = \frac{12 x}{x ^{2} - 4} : \frac{df ( x )}{d x} = \frac{12 ( - x ^{2} - 4 )}{( x ^{2} - 4 ) ^{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{5}{3}

Find the line with slope m=

- \frac{5}{3}

and passing through

(4, 4) : y = - \frac{5}{3} x + \frac{32}{3}

y = - \frac{5}{3} x + \frac{32}{3}

What is the tangent of f(x)=(12x)/(x^2-4),(4,4) ?
The tangent of f(x)=(12x)/(x^2-4),(4,4) is y=-5/3 x+32/3