Hi not sure if I've got this right.

Determine any points at which the gradient of $\displaystyle y=x^3-3x^2-1$ is zero, and detemine whether these are maxima, minima or points of inflection.

$\displaystyle 3x^2 - 6x$

$\displaystyle 3x(x-2)$

x = 2

$\displaystyle (2)^3-3(2)^2-1$

(2, -5)

(left of turning point) x = 1

$\displaystyle 3(1)^2-6(1)= -3$

(1, -3)

(right of turning point) x = 3

$\displaystyle 3(3)^2-6(3)= -9$

(1, -9)

I'm not sure if I've done this right, but if I were to answer this I believe (2, -5) is minima.