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Without a calculator, determine the minimum value of  for . Use the second derivative to justify that your value is a minimum.

Find and .

Identify candidates for minimum values by finding where and where DNE. Note: this includes the endpoints.

Evaluate all candidates (except for the endpoints) in the 2nd derivative.
Recall that a LOCAL minimum will exist where or DNE and .
Note: endpoints can be global (not local) minima.

To find the GLOBAL minimum, evaluate and compare (local minimum) with (endpoint) and (endpoint ).
The lowest value is the global minimum.

Compute without a calculator