AP Calculus BC / Unit 5: Analytical Applications of Differentiation
5.5 Using the Candidates Test to Determine Absolute (Global) Extrema
Notes
On a closed interval $[a,b]$: find the critical points inside, evaluate $f$ at those points and at both endpoints, then compare. The largest is the absolute max; the smallest is the absolute min.
Practice
Absolute max of $f(x)=x^2-4x$ on $[0,5]$?
Candidates: $f(0)=0$, $f(2)=-4$, $f(5)=5$.
Absolute min of that same function on $[0,5]$?
The critical point at $x=2$ gives $-4$.
Why must endpoints be checked?
A function can be largest at an edge with no horizontal tangent.
Ready for more? Take the Unit 5 test.