Discussion
True or false: the vanishing of the first derivative at a point guarantees an extremum there.
Answer: B
The condition is necessary for an interior extremum of a differentiable function but not sufficient. The function \( y = x^{3} \) has \( y' = 0 \) at the origin yet rises through it, the point being a horizontal inflexion. Deciding which case holds needs the second derivative, or the first non-vanishing one
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