A function of one argument is minimized when the first derivative is:
A) zero and the second derivative is positive.
B) positive and the second derivative is negative.
C) zero and the second derivative is negative.
D) negative and the second derivative is positive.
E) zero and the second derivative is zero.

Question

Quizplus · Accepted Answer

In calculus, we know that if the first derivative of a function is zero, it means that the function is either at a minimum, maximum or a point of inflection. We need to further analyze if the second derivative is positive or negative to know what kind of point it is. If the second derivative is positive, then we have a minimum point. If the second derivative is negative, then we have a maximum point. Therefore, to find the minimum point, we need the first derivative to be zero and the second derivative to be positive.

A Function of One Argument Is Minimized When the First