Optimization calculator

How to find max and min

1. Find f'(x) and set it equal to 0 to get critical points.

2. Use the second derivative test: if f''(c) > 0, it's a minimum; if f''(c) < 0, it's a maximum.

3. Check endpoints if the domain is bounded.

First vs second derivative test

First derivative test: Check if f' changes sign at the critical point. + to − = max, − to + = min.

Second derivative test: Evaluate f'' at the critical point. Faster but inconclusive when f'' = 0.

Global vs local extrema

Local: Highest/lowest in a neighborhood. Found by derivative tests.

Global: Highest/lowest overall. Compare all local extrema and endpoint values.