Find the coordinates of the stationary points on the curve y=x(x-2)^4. Determine the nature of the stationary points.
I am able to find the stationary points are at x=2 and x=0.4
When x=0.4, the second derivative of y=-20.48, hence it is a max point.
When x=2, the second derivative of y =0, which means it is point of inflexion. However, when I plotted the graph of y, I realise that it is a minimum point. Which is correct?
The fact that the second derivative is 0 does NOT mean it is an inflection point. An inflection point is where the second derivative changes sign. Of course, for a smooth function, that can only happen where the second derivative is 0 but the converse is not necessarily true.