Find the stationary point on the curve y=x^2-1 and show that it is a minimum point by checking the derivative on both sides of it.

Question

I've found that its stationary point is (0, -1), just don't understand what "check the derivatives of both sides of it" means..

Answer 1

draw the curve. If it's a minimum at (0,-1) then
(a) y will have negative slope on the left: y' < 0
(b) y will have positive slope on the right: y' > 0
That is, y will be decreasing, hit the minimum, and then start increasing

FYI, if y" > 0 at x=0, then the graph is concave up, so it is a minimum there.