Question

Why must the left endpoint \[a\] and right endpoint \[b\] be checked for absolute extrema on \[[a,b]\]?

Options

• The largest or smallest value may occur at an endpoint.

• The second derivative is always zero at an endpoint.

• The derivative always does not exist at an endpoint.

• Every endpoint is a critical point.

Answer 1

A critical point inside the interval is not the only possible location of an absolute extremum. The largest or smallest value may instead occur at \[a\] or \[b\].