# parametric curves

• Aug 6th 2008, 07:48 PM
cityismine
parametric curves
x=t^2
y=t^3-3t

a) Show that C has two tangents at the point (3,0) and find their equation.
b) Find the point on C where the tangent is horizontal or vertical.
c) Determine where the curve is concave upward or downward?

I was able to do part a and b, but I'm stuck on part c. How do you find the second derivative of this curve?
• Aug 6th 2008, 08:00 PM
mr fantastic
Quote:

Originally Posted by cityismine
x=t^2
y=t^3-3t

a) Show that C has two tangents at the point (3,0) and find their equation.
b) Find the point on C where the tangent is horizontal or vertical.
c) Determine where the curve is concave upward or downward?

I was able to do part a and b, but I'm stuck on part c. How do you find the second derivative of this curve?

$\displaystyle \frac{d^2 y}{d x^2} = \frac{d}{dx} \left[ \frac{dy}{dx}\right] = \frac{d}{dt} \left[ \frac{dy}{dx}\right] \cdot \frac{dt}{dx} \, ......$
• Aug 6th 2008, 10:21 PM
cityismine
That's the formula I'm having trouble understanding. But I googled some examples and I think I get it now. It's the derivative of the 1st derivative divided by the denominator of the first derivative, right?
• Aug 6th 2008, 10:35 PM
mr fantastic
Quote:

Originally Posted by cityismine and edited (in red) by Mr F
That's the formula I'm having trouble understanding. But I googled some examples and I think I get it now. It's the derivative with respect to t of dy/dx divided by dx/dt, right?

Right.