What is the tangent of f(x)=(10x)/(x^2-6),(4,4) ?

The tangent of f(x)=(10x)/(x^2-6),(4,4) is y=-11/5 x+64/5

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tangent of f(x)=(10x)/(x^2-6),(4,4)

tangent of

f (x) = \frac{10 x}{x ^{2} - 6}, (4, 4)

y = - \frac{11}{5} x + \frac{64}{5}

Solution steps

Find the slope of

f (x) = \frac{10 x}{x ^{2} - 6} : \frac{df ( x )}{d x} = \frac{10 ( - x ^{2} - 6 )}{( x ^{2} - 6 ) ^{2}}

Compute the slope of

f (x) = \frac{10 x}{x ^{2} - 6}

(4, 4) : m = - \frac{11}{5}

Find the line with slope m=

- \frac{11}{5}

and passing through

(4, 4) : y = - \frac{11}{5} x + \frac{64}{5}

y = - \frac{11}{5} x + \frac{64}{5}

4 x^{2} - 3

y = x^{2} + 4 x + 3

n = 0 \sum \infty sin (\frac{1}{n ^{2}})

x \to 0 lim (\frac{\frac{1}{1 + x} - 1}{x})

What is the tangent of f(x)=(10x)/(x^2-6),(4,4) ?
The tangent of f(x)=(10x)/(x^2-6),(4,4) is y=-11/5 x+64/5