I keep getting “Critical points” questions wrong in Application of Derivatives. What's the trap?
thinking every point where f'(x)=0 is a maximum.
The usual trap: thinking every point where f'(x)=0 is a maximum. How to avoid it: f'(x)=0 finds candidates; a further test says max, min or neither. Go back to the definition — at a maximum or minimum of a smooth function the derivative is zero (the tangent is flat).
Key point
Critical points
Common mistake
thinking every point where f'(x)=0 is a maximum.
Memory tip
f'(x)=0 finds candidates; a further test says max, min or neither.
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