Finding Absolute (Global) Extreme Values over Closed Intervals (Calculus Problems and Solutions)

The First Derivative Test classifies a critical point of a function based on the behavior of the first derivative of the function near the critical point, while the Second Derivative Test does so based on the behavior of the second derivative of the function near the critical point.

#calculus #optimization #CriticalPoint

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(0:00) Optimize f(x)=x^3-3x^2+20 over [-2,5/2] (closed and bounded, or compact, interval). Also graph it and find the best possible bounds (best possible upper bound and best possible lower bound).
(7:42) Optimize f(x)=x*e^(-x^2/2) over [-2,2]
(14:23) Optimize f(x)=3x^(1/3)-x over [-1,8]
(22:03) Optimize f(x)=(sin(x))^2-cos(x) over [0,pi]
(28:18) Optimize f(x)=(10x-x^2)^(2/3) over [-1,8]
(35:00) Story problem: inventory optimization (minimize cost)

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