Exercise · ZW-FIRST-ORDER-NECESSARY-CONDITION-005 · ★☆☆ Basic

What kind of candidate points does the first-order condition identify for an unconstrained differentiable function?

Choose one option.

Show answer
  • B. Critical points, where the gradient is zero

Explanation

The condition identifies the points where the gradient vanishes as candidates for optima.

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Review the concept: First-order necessary condition

A first-order necessary condition states that if \(x^*\) is a local minimizer of a differentiable function \(f\), then \(\nabla f(x^*)=0\).

\[x^* \text{ mín. local} \Rightarrow \nabla f(x^*) = 0\]

More practice problems: first-order necessary condition

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