What is the tangent of f(x)=(2x)/(x^2-7),\at x=3 ?

The tangent of f(x)=(2x)/(x^2-7),\at x=3 is y=-8x+27

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tangent of f(x)=(2x)/(x^2-7),\at x=3

tangent of

f (x) = \frac{2 x}{x ^{2} - 7}, at x = 3

y = - 8 x + 27

Solution steps

Find the tangent point:

(3, 3)

Find the slope of

f (x) = \frac{2 x}{x ^{2} - 7} : \frac{df ( x )}{d x} = \frac{2 ( - x ^{2} - 7 )}{( x ^{2} - 7 ) ^{2}}

Compute the slope of

f (x) = \frac{2 x}{x ^{2} - 7}

x = 3 : m = - 8

Find the line with slope m=

- 8

and passing through

(3, 3) : y = - 8 x + 27

y = - 8 x + 27

\int \frac{sin ( 3 x )}{3 cos ( 3 x )} d x

\int x^{2} e^{15 x} d x

\int (1 + 3 t) t^{2} d t

x \to \infty lim (x e^{- x})

\frac{d}{d x} (tan (0))

What is the tangent of f(x)=(2x)/(x^2-7),\at x=3 ?
The tangent of f(x)=(2x)/(x^2-7),\at x=3 is y=-8x+27