Part 3/7:
Most of the time, the derivative ( f'(x) ) at these extreme points is equal to zero, indicating a flat tangent line at these points. However, it's essential to recognize that there are exceptions—consider the absolute value function, ( y = |x| ) at ( x=0 ), where the derivative is undefined, yet it's still a local minimum.
Absolute Maximums and Minimums
Unlike local extrema, absolute maximums and minimums assess global behavior over a defined interval, determining the highest and lowest points of a function. The absolute maximum (( \text{ABS Max} )) is the greatest y-value in the interval, while the absolute minimum (( \text{ABS Min} )) is the least y-value.