What is the tangent of f(x)=(7x)/(x-3),\at x=6 ?

The tangent of f(x)=(7x)/(x-3),\at x=6 is y=-7/3 x+28

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tangent of f(x)=(7x)/(x-3),\at x=6

tangent of

f (x) = \frac{7 x}{x - 3}, at x = 6

y = - \frac{7}{3} x + 28

Solution steps

Find the tangent point:

(6, 14)

Find the slope of

f (x) = \frac{7 x}{x - 3} : \frac{df ( x )}{d x} = - \frac{21}{( x - 3 ) ^{2}}

Compute the slope of

f (x) = \frac{7 x}{x - 3}

x = 6 : m = - \frac{7}{3}

Find the line with slope m=

- \frac{7}{3}

and passing through

(6, 14) : y = - \frac{7}{3} x + 28

y = - \frac{7}{3} x + 28

2 + 5 tan^{- 1} (\frac{x}{2})

\int (9 e^{x} - 9 x) d x

x^{3} e^{6 x^{3} + 8 x^{2} - 7}

\frac{d}{d x} (arcsin (x^{3}))

f (x) = \frac{f ( x )}{x ^{2} + 2}

What is the tangent of f(x)=(7x)/(x-3),\at x=6 ?
The tangent of f(x)=(7x)/(x-3),\at x=6 is y=-7/3 x+28