Question about using $y''$ to determinenature of stat points

Can you use $y''$ to determine the nature of stationary points?  YES

• If $y''<0$ for some stat point then it is a MAX (Concave down).
• If $y''>0$ for some stat point then it is a MIN (Concave up).
• If $y''=0$ for some stat point then you MUST use the first derivative test box to see what it is :-)

EXAMPLE: $y=x^2-1$

$y'=2x$  stationary point is when $x=0$

Here, $y''=2>0$.

$(0,-1)$ is the stat point.

Since $y''(0)=2$ , so $y''>0$ and hence its a MIN.

You can verify this with the first derivative test.

JH :-)