What is the normal of y= x/a+a/x ,\at x= a/2 ?

The normal of y= x/a+a/x ,\at x= a/2 is y= a/3 x+5/2-(a^2)/6

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normal of y= x/a+a/x ,\at x= a/2

normal of

y = \frac{x}{a} + \frac{a}{x}, at x = \frac{a}{2}

y = \frac{a}{3} x + \frac{5}{2} - \frac{a ^{2}}{6}

Solution steps

Find the tangent point:

(\frac{a}{2}, \frac{5}{2})

Find the slope of

y = \frac{x}{a} + \frac{a}{x} : \frac{d y}{d x} = \frac{1}{a} - \frac{a}{x ^{2}}

Compute the slope of

y = \frac{x}{a} + \frac{a}{x}

x = \frac{a}{2} : m = - \frac{3}{a}

Compute the slope of the perpendicular line:

m_{p} = \frac{a}{3}

Find the line with slope m=

\frac{a}{3}

and passing through

(\frac{a}{2}, \frac{5}{2}) : y = \frac{a}{3} x + \frac{5}{2} - \frac{a ^{2}}{6}

y = \frac{a}{3} x + \frac{5}{2} - \frac{a ^{2}}{6}

x \to 5 lim ([x])

f (x) = x^{2} + 8, (- 3, 17)

x \to - 2 lim (4 x)

y^{^{'}} - 2 (x + 1)^{3} = \frac{4}{( x + 1 )} y

\frac{d}{d x} (x^{5} x)

What is the normal of y= x/a+a/x ,\at x= a/2 ?
The normal of y= x/a+a/x ,\at x= a/2 is y= a/3 x+5/2-(a^2)/6