For a differentiable function defined on the interval
MATHEMATICS · Single correct · CBSE · Mathematics · Applications of Derivatives · Applications of Derivatives
Problem
For a differentiable function f defined on the interval (−5,5), the sign of f′(x) is given by
x<−2: f′(x)<0x=−2: f′(x)=0−2<x<1: f′(x)>0x=1: f′(x)=0x>1: f′(x)<0
Which of the following statements about f is most strongly supported by the information above?
(a) f has a relative maximum at x=−2 and a relative minimum at x=1.
(b) f has relative minima at both x=−2 and x=1.
(c) f has a relative minimum at x=−2 and a relative maximum at x=1.
(d) f is concave up at both x=−2 and x=1.