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

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

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

tangent of

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

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

Solution steps

Find the tangent point:

(4, 4)

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}

x = 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}

h \to 0 lim (\frac{- 8 + h}{h})

(e^{- \frac{1}{x ^{2}}})^{^{'}}

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

\int_{2}^{3} \frac{5}{3 - x} d x

\frac{\partial}{\partial x} (x^{2} \cdot y^{3})

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