1. The curve C has equation y = 3x^4 – 8x^3 – 3 (a) Find (i) d d y x (ii) d d 2 y x 2 (3) (b) Verify that C has a stationary point when x = 2 (2) (c) Determine the nature of this stationary point, giving a reason for your answer.

To differentiate use formula.

multiply factor by power then minus one from power (where x is invloved)

dy/dx = 12x^3 - 24x^2

d^2y/dx^2 = 36x^2 - 48x (this is just a further differentiation)

b) to find stationary point, put value of x into gradient equation (dy/dx) and it should equal to zero (hence stationary)

c) put value of x into second derivative. answer = 48 = positive hence the nature of this point is positive