MATHEMATICS · Subjective · CBSE · Mathematics · Applications of Derivatives · Applications of Derivatives
Problem
On the interval [−4,6], the derivative of a continuous function q satisfies q′(x)=0 only at x=2. In addition,
q′′(x)<0 for −4<x<1,
q′′(x)>0 for 1<x<4, and
q′′(x)<0 for 4<x<6.
Determine whether q attains an absolute maximum, an absolute minimum, or neither at x=2 on [−4,6]. Provide a brief justification.