Find the stationary points and their nature of the curve y = 3x^3 - 7x + 2x^-1
To start, we need to know that the gradient of the curve at the stationary points is 0 and that when the second derivative is less than 0, there is a maximum and when the derivative is greater than 0, there is a minimum. In order to find the gradient of the curve, we differentiate y. This gives dy/dx = 9x2 - 7 - 2x-2.We know that at the stationary points, dy/dx = 0. Hence, 9x2 - 7 - 2x-2 = 0 and x = 1, -1. To find the nature of these points, we need to differentiate one more time and substitute the values of x into the second derivative. d2y/dx2= 18x + 4x-3.For x = 1, d2y/dx2= 22. Therefore at x = 1, there is a minimum.For x = -1, d2y/dx2= -22. Therefore at x = -1, there is a maximum.
