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

The tangent of f(x)= 2/(sqrt(x)),\at x=3 is y=-1/(3sqrt(3))x+sqrt(3)

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

tangent of

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

y = - \frac{1}{3 3} x + 3

Solution steps

Find the tangent point:

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

Find the slope of

f (x) = \frac{2}{x} : \frac{df ( x )}{d x} = - \frac{1}{x ^{\frac{3}{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{1}{3 3}

Find the line with slope m=

- \frac{1}{3 3}

and passing through

(3, \frac{2}{3}) : y = - \frac{1}{3 3} x + 3

y = - \frac{1}{3 3} x + 3

t^{- 1}

\frac{d}{d x} (x^{3} + 2)

x \to 0 lim (\frac{e ^{- 4 x} - 1}{x})

3 e^{x} + \frac{2}{3 x}

\frac{\partial}{\partial y} (x + 2 y - 1)

What is the tangent of f(x)= 2/(sqrt(x)),\at x=3 ?
The tangent of f(x)= 2/(sqrt(x)),\at x=3 is y=-1/(3sqrt(3))x+sqrt(3)