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

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

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

tangent of

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

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

Solution steps

Find the tangent point:

(4, 4)

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}

x = 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}

\int (2 x + 3) sin (3 x) d x

\frac{( - 1 ) ^{n} x ^{n}}{n !}

\int \frac{x}{( 5 - 4 x - x ^{2} ) ^{\frac{3}{2}}} d x

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g (w) = \frac{8}{3 w ^{5}} + 9 w

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