A curve has the equation y=3 + x^2 -2x^3. Find the two stationary points of this curve.
At stationary point the derivative of y with respect to x equals zero. Find dy/dx. dy/dx = 2x - 6x2.Set dy/dx = 0 ,giving 2x - 6x2 = 0. We can rearrange this to x(1-3x) = 0 and solve the equation for x. This results in x1 = 0 and x2 = 1/3.Substitute these x values into the original equation and we get the corresponding y values for the coordinates. y1 = 3 + (0)2 - 2(0)3 = 3. y2 = 3 +(1/3)2 - 2(1/3)3 = 82/27. Giving the coordinates for the two stationary points as p1= (0,3) and p2 = (1/3,82/27).
TC
