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

The tangent of f(x)=(12)/(x^2-4),(4,4) is y=1.57694…x-2.30777… \lor y=0.38381…x+2.46473…

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

tangent of

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

y = 1.57694 \dots x - 2.30777 \dots or y = 0.38381 \dots x + 2.46473 \dots

Solution steps

Slope of the tangent line at

(4, 4) : m = \frac{- 4 x ^{2} + 28}{( x ^{2} - 4 ) ( x - 4 )}

Find the slope of

f (x) = \frac{12}{x ^{2} - 4} : m = - \frac{24 x}{( x ^{2} - 4 ) ^{2}}

Solve

- \frac{24 x}{( x ^{2} - 4 ) ^{2}} = \frac{- 4 x ^{2} + 28}{( x ^{2} - 4 ) ( x - 4 )} : x \approx - 0.76569 \dots, x \approx - 4.57268 \dots

Find the tangent line at

x = - 0.76569 \dots : y = 1.57694 \dots x - 2.30777 \dots

Find the tangent line at

x = - 4.57268 \dots : y = 0.38381 \dots x + 2.46473 \dots

y = 1.57694 \dots x - 2.30777 \dots or y = 0.38381 \dots x + 2.46473 \dots

What is the tangent of f(x)=(12)/(x^2-4),(4,4) ?
The tangent of f(x)=(12)/(x^2-4),(4,4) is y=1.57694…x-2.30777… \lor y=0.38381…x+2.46473…