MATHEMATICS · Single correct · CBSE · Mathematics · Applications of Derivatives · Applications of Derivatives
Problem
For a function f defined and continuous on (−∞,∞), the derivative f′(x) satisfies the following.
• f′(x)<0 for x<−3
• f′(x)>0 for −3<x<0
• f′(x)<0 for 0<x<5
• f′(x)>0 for x>5
• f′(x)=0 at x=−3 and x=5
• f′(x) is undefined at x=0
Which of the following describes the relative extrema of f?
(a) Relative maximum at x=−3, relative minimum at x=0, and relative maximum at x=5.
(b) Relative minimum at x=−3, relative maximum at x=0, and relative minimum at x=5.
(c) Relative minimum at x=−3, relative minimum at x=0, and relative maximum at x=5.
(d) Relative minimum at x=−3, no relative extremum at x=0, and relative minimum at x=5.