What is the tangent of f(x)= 3/(x^{1/2)} ?

The tangent of f(x)= 3/(x^{1/2)} is y=-3/(2a_{0)^{3/2}}x+9/(2a_{0)^{1/2}}

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tangent of f(x)= 3/(x^{1/2)}

tangent of

f (x) = \frac{3}{x ^{\frac{1}{2}}}

y = - \frac{3}{2 a _{0}^{\frac{3}{2}}} x + \frac{9}{2 a _{0}^{\frac{1}{2}}}

Solution steps

Compute the tangent line to the general point

x = a_{0}

Find the tangent point:

(a_{0}, \frac{3}{a _{0}^{\frac{1}{2}}})

Find the slope of

f (x) = \frac{3}{x ^{\frac{1}{2}}} : \frac{df ( x )}{d x} = - \frac{3}{2 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{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}^{\frac{1}{2}}}) : y = - \frac{3}{2 a _{0}^{\frac{3}{2}}} x + \frac{9}{2 a _{0}^{\frac{1}{2}}}

y = - \frac{3}{2 a _{0}^{\frac{3}{2}}} x + \frac{9}{2 a _{0}^{\frac{1}{2}}}

x \to 3 + lim (\frac{x + 2}{x + 3})

s l o p e (- 6, - 7), (- 24, - 7)

\int e^{3 x} e^{- 5 x} d x

\frac{\partial}{\partial x} (\frac{x - y}{30 - y})

\frac{d}{d x} (ln (3^{x} sec^{3} (4 x)))

What is the tangent of f(x)= 3/(x^{1/2)} ?
The tangent of f(x)= 3/(x^{1/2)} is y=-3/(2a_{0)^{3/2}}x+9/(2a_{0)^{1/2}}