What is the tangent of y= 3/x ,\at P(0.5,6) ?

The tangent of y= 3/x ,\at P(0.5,6) is y=-3/(a_{0)^2}x+6/(a_{0)}

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tangent of y= 3/x ,\at P(0.5,6)

tangent of

y = \frac{3}{x}, at P (0.5, 6)

y = - \frac{3}{a _{0}^{2}} x + \frac{6}{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

y = \frac{3}{x} : \frac{d y}{d x} = - \frac{3}{x ^{2}}

Compute the slope of

y = \frac{3}{x}

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

Find the line with slope m=

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

and passing through

(a_{0}, \frac{3}{a _{0}}) : y = - \frac{3}{a _{0}^{2}} x + \frac{6}{a _{0}}

y = - \frac{3}{a _{0}^{2}} x + \frac{6}{a _{0}}

\frac{d y}{d x} = - 3 x y^{3}

x \to 1 lim (x^{2} - 3)

4 y^{^{''}} - 4 y^{^{'}} + 2 y = 0

\frac{x}{x - 1}

\int \frac{x}{e ^{7 x}} d x

What is the tangent of y= 3/x ,\at P(0.5,6) ?
The tangent of y= 3/x ,\at P(0.5,6) is y=-3/(a_{0)^2}x+6/(a_{0)}