Question

A curve has equation y=8/x +2x.
(i) Find the dy/dx and d^2y/dx^2.
(ii) Find the coordinates of the stationary points and state,with a reason,the nature of each stationary point.

Answer 1

We know that at stationary points, dy/dx = 0 (since the gradient is zero at stationary points). By differentiating, we get: dy/dx = 2x. Therefore the stationary points on this graph occur when 2x = 0, which is when x = 0. When x = 0, y = 0, therefore the coordinates of the stationary point are (0,0).

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