Mathematics

To find local extrema, you need to locate where the derivative equals zero—these are your candidate points. Then use the second derivative test to classify each: if $f''(x) > 0$, you have a local minimum (curve bends upward); if $f''(x) < 0$, you have a local maximum (curve bends downward). This approach turns a shape-sketching problem into straightforward algebra.

To find local extrema, you need to locate where the derivative equals zero—these are your candidate points. Then use the second derivative test to classify each: if $f''(x) > 0$, you have a local minimum (curve bends upward); if $f''(x) < 0$, you have a local maximum (curve bends downward). This approach turns a shape-sketching problem into straightforward algebra.