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MCQ
Wrong
\(f\) continuous on \([a,b]\) has rel max at \(c\), \(a < c < b\). Which true? I. \(f'(c)\) exists II. If \(f'(c)\) exists, \(f'(c)=0\) III. If \(f''(c)\) exists, \(f''(c) \leq 0\)
A
II only
B
III only
C
I and II only
D
I and III only
II and III only
Correct Answer
Explanation
I: not necessarily (corner). II: yes (Fermat). III: yes (concavity at max).