steepest slope for the time response of the comparator

[joehwang]

Hi,
I am calculating the steepest slope for the output time response of the the two-stage open-loop comparator. From the book (Allen, P.448, Eq.8.2-13), it says I need to find it by differentiating the equation of time response twice and setting the result the result = 0. Why???
I know the slope can be found by differentiating once. Differentiating twice is for the variation of the slpoe. Why the steepest slope can be found by setting the variation of the slope to 0?

Thanks!

 

[kienhuy]

Setting the second derivative to zero finds the local max/min of the first derivative, which in other words is finding the steepest slope.