In order to find whether a local minimum is a global minimum, one must
A) set the second derivative to 0 and solve for $\mathrm{x}$ and check whether the first derivative is negative at that $\mathrm{x}$
B) check whether the second derivative is negative at the value of $x$ corresponding to the local minimum
C) set the second derivative to 0 and solve for $\mathrm{x}$ and check whether the first derivative is positive at that $\mathrm{x}$
D) check whether the second derivative is positive at the value of $x$ corresponding to the local minimum

Question

Quizplus · Accepted Answer

A positive second derivative at a point indicates that the function is concave up at that point, suggesting a local minimum. However, to determine if a local minimum is also a global minimum, one must examine the function's behavior over its entire domain, not just through the second derivative test. The second derivative test can confirm if a point is a local minimum by showing concavity, but additional analysis is required to establish global minimality.

In Order to Find Whether a Local Minimum Is a Global