What is the tangent of f(x)= 3/(sqrt(x)) ?

The tangent of f(x)= 3/(sqrt(x)) is y=-3/(2a_{0)^{3/2}}x+9/(2sqrt(a_{0))}

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tangent of f(x)= 3/(sqrt(x))

tangent of

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

y = - \frac{3}{2 a _{0}^{\frac{3}{2}}} x + \frac{9}{2 a _{0}}

Solution steps

Compute the tangent line to the general point

x = a_{0}

Find the tangent point:

(a_{0}, \frac{3}{a _{0}})

Find the slope of

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

Compute the slope of

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

x = a_{0} : m = - \frac{3}{2 a _{0}^{\frac{3}{2}}}

Find the line with slope m=

- \frac{3}{2 a _{0}^{\frac{3}{2}}}

and passing through

(a_{0}, \frac{3}{a _{0}}) : y = - \frac{3}{2 a _{0}^{\frac{3}{2}}} x + \frac{9}{2 a _{0}}

y = - \frac{3}{2 a _{0}^{\frac{3}{2}}} x + \frac{9}{2 a _{0}}

\frac{\partial}{\partial y} (6 x^{\frac{1}{3}} y^{\frac{2}{3}})

\frac{\partial}{\partial x} (\frac{4 x}{( y + 2 z ) ^{3}})

x \to 0 lim (\frac{1}{x} sin (x))

\int_{0}^{3 π} ∣ sin (x) ∣ d x

\frac{d}{d x} (\frac{2 x}{x - 3})

What is the tangent of f(x)= 3/(sqrt(x)) ?
The tangent of f(x)= 3/(sqrt(x)) is y=-3/(2a_{0)^{3/2}}x+9/(2sqrt(a_{0))}