The Curve C has equation y = 3x^4 - 8x^3 -3. Find the first and second derivative w.r.t x and verify that y has a stationary point when x = 2. Determine the nature of this stationary point, giving a reason for your answer.
The first derivative is otherwise denoted by dy/dx.dy/dx = 12x^3 -24x^2.The second derivative is denoted by d2y/dx2, otherwise known as the first derivative of the function dy/dx.d2y/dx2 = 36x^2 - 48x.A stationary point exists if dy/dx = 0 has a valid solution for x. dy/dx = 12x^3 -24x^2 = 0 ==> x = 0 and x = 2. (Check by substitution (dy/dx at x =2) and by finding the solution for dy/dx = 0).Substitute x =2 into d2y/dx2 = 36x^2 - 48x. The result is at x =2, d2y/dx2 is 48 > 0 and hence this stationary point is classified as a minima / minimum.
