# Math Help - Graphing Using Calculus

1. ## Graphing Using Calculus

y^2 = (a^2 x) / (2a - x )

Find points of inflexion and sketch the curve.

By implicitly differentiating Ive got a value for dy/dx

= 2a^3 / (2a-x)^2 ( 2y)

However, I do not know how to do from here. Do I implicitly differentiate again or ... and how do i do that?

2. Originally Posted by Lukybear
y^2 = (a^2 x) / (2a - x )

Find points of inflexion and sketch the curve.

By implicitly differentiating Ive got a value for dy/dx

= 2a^3 / (2a-x)^2 ( 2y)

However, I do not know how to do from here. Do I implicitly differentiate again or ... and how do i do that?
First of all, the graph is defined for 0<= x<=2a

$y=\sqrt{\frac{a^2x}{2a-x}}$ , 0<= x<=2a

$\frac{dy}{dx}=\sqrt{\frac{a^4}{(2a-x)^3x}}$

$\frac{d^2y}{dx^2}=\frac{1}{2}\sqrt{\frac{1}{(2a-x)^5x^3}}\cdot (-4x+2a)$

Set that equals 0, x=1/2 a

Hence the point of inflection is (1/2 a , a sqrt(1/3))