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

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

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

tangent of

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

y = - \frac{7}{4 2} x + \frac{5}{2 2}

Solution steps

Find the tangent point:

(2, - \frac{1}{2})

Find the slope of

f (x) = \frac{x}{3 x - 8} : \frac{df ( x )}{d x} = \frac{- 3 x - 8}{2 x ( 3 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 2}

Find the line with slope m=

- \frac{7}{4 2}

and passing through

(2, - \frac{1}{2}) : y = - \frac{7}{4 2} x + \frac{5}{2 2}

y = - \frac{7}{4 2} x + \frac{5}{2 2}

y^{^{''}} - 5 y^{^{'}} + 6.25 y = 0, y (0) = 1, y^{^{'}} (0) = 0.5

x \to \infty lim (e^{x} + 1)

\int_{π}^{2 π} sin (x) d x

\frac{d}{d x} (e^{4 - x})

\frac{d}{d x} (ln (sin (5 x)))

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