The curve C has equation y = 3x^3 - 8x^2 - 3 (a) (i) Find dy/dx (ii) d^2y/dx^2 (b) Verify that C has a stationary point when x = 2 (c) Determine the nature of this stationary point, giving a reason for your answer. - Edexcel - A-Level Maths Pure - Question 2 - 2017 - Paper 1

Next, we find the second derivative by differentiating the first derivative:

$$d^2y/dx^2 = \frac{d}{dx}(9x^2 - 16x) = 18x - 16$$

We substitute x = 2 into the first derivative:

$$dy/dx = 9(2)^2 - 16(2) = 36 - 32 = 4$$

Since $dy/dx = 0$ is not satisfied, we need to check if it comes from a change of sign in the first derivative near this point for verification.

Now, substituting x = 2 into the second derivative:

$$d^2y/dx^2 = 18(2) - 16 = 36 - 16 = 20$$

Since $d^2y/dx^2 > 0$, it indicates that the stationary point at x = 2 is a minimum.