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}}

Compute the slope of

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

(4, 4) : 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}

\int \frac{2}{x ^{2} 1 + x ^{2}} d x

\frac{8 x ^{2} + 9}{x ^{2} + 5}

45

\frac{3}{x ^{9}}

y^{^{'}} = 7 x + y, y (0) = 9

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