# Math Help - Differentiation

1. ## Differentiation

Find the values of t when the function defined by x = 5t^3 + 2 and y = 3t^2 -5t is concave down.

2. Refer this site: Sign of 2nd derivative, Maths First, Institute of Fundamental Sciences, Massey University

Concave down = Slopes decreasing

$\frac{dx}{dt}=15t^2$

$\frac{d^2x}{dt^2}=30t$

$\frac{dy}{dt}=6t-5$

$\frac{d^2y}{dt^2}=6$

$\frac{d^2y}{dx^2}=\frac{6}{30t}$

Since the slopes are decreasing,

$\frac{d^2y}{dx^2}<0$

$\frac{6}{30t}<0$

$t<0$

3. Thanks, I kinda understand what the questions asking but I don't think I'd be able to answer it in a test lol, didn't realise it was an excellence question, nvm. :]