What is the tangent of 5/(sqrt(x)),\at m ?

The tangent of 5/(sqrt(x)),\at m is m=-5/(2a_{0)^{3/2}}x+(15)/(2sqrt(a_{0))}

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tangent of 5/(sqrt(x)),\at m

tangent of

\frac{5}{x}, at m

m = - \frac{5}{2 a _{0}^{\frac{3}{2}}} x + \frac{15}{2 a _{0}}

Solution steps

Compute the tangent line to the general point

x = a_{0}

Find the tangent point:

(a_{0}, \frac{5}{a _{0}})

Find the slope of

m = \frac{5}{x} : \frac{d m}{d x} = - \frac{5}{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{5}{2 a _{0}^{\frac{3}{2}}}

Find the line with slope m=

- \frac{5}{2 a _{0}^{\frac{3}{2}}}

and passing through

(a_{0}, \frac{5}{a _{0}}) : m = - \frac{5}{2 a _{0}^{\frac{3}{2}}} x + \frac{15}{2 a _{0}}

m = - \frac{5}{2 a _{0}^{\frac{3}{2}}} x + \frac{15}{2 a _{0}}

n = 0 \sum \infty (\frac{( - 1 ) ^{n}}{2 ^{n}}) x^{2 n}

\frac{d y}{d x} = x (x - 2)

ln (6 x)

(x + y + 4 d x) + (2 x + 2 y + 1 d y) = 0

f (x) = 4 e^{x} + x, (0, 4)

What is the tangent of 5/(sqrt(x)),\at m ?
The tangent of 5/(sqrt(x)),\at m is m=-5/(2a_{0)^{3/2}}x+(15)/(2sqrt(a_{0))}