What is the tangent of f(x)=(sqrt(x))/(2x-8),\at x=3 ?

The tangent of f(x)=(sqrt(x))/(2x-8),\at x=3 is y=-7/(4sqrt(3))x+(5sqrt(3))/4

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tangent of f(x)=(sqrt(x))/(2x-8),\at x=3

tangent of

f (x) = \frac{x}{2 x - 8}, at x = 3

y = - \frac{7}{4 3} x + \frac{5 3}{4}

Solution steps

Find the tangent point:

(3, - \frac{3}{2})

Find the slope of

f (x) = \frac{x}{2 x - 8} : \frac{df ( x )}{d x} = \frac{- x - 4}{x ( 2 x - 8 ) ^{2}}

EN : T i tl e G e n er a l Eq u a t i o n Sl o p e A t P o in t 2 Eq : m = - \frac{7}{4 3}

Find the line with slope m=

- \frac{7}{4 3}

and passing through

(3, - \frac{3}{2}) : y = - \frac{7}{4 3} x + \frac{5 3}{4}

y = - \frac{7}{4 3} x + \frac{5 3}{4}

x \to \infty lim (\frac{5}{x} - 4)

y = \frac{ln ( x )}{x ^{9}}

\int \frac{1}{2} ln (x) d x

\frac{d}{d x} (- 8 e^{- x})

4 x^{^{''}} + 2 x^{^{'}} + 4 x = 100, x (0) = 5, x^{^{'}} (0) = 0

What is the tangent of f(x)=(sqrt(x))/(2x-8),\at x=3 ?
The tangent of f(x)=(sqrt(x))/(2x-8),\at x=3 is y=-7/(4sqrt(3))x+(5sqrt(3))/4