Which of the following statements best describes the relationship between the sign of…
MATHEMATICS · Single correct · CBSE · Mathematics · Applications of Derivatives · Applications of Derivatives
Problem
Which of the following statements best describes the relationship between the sign of f′′(x) and the concavity of the graph of y=f(x) on an open interval?
(a) If f′′(x)=0 throughout the interval, the graph is concave up on that interval.
(b) If f′′(x)<0 throughout the interval, the graph is concave up on that interval.
(c) If f′′(x)>0 throughout the interval, the graph is concave up on that interval.
(d) If f′′(x)=0 at a point in the interval, the graph must have an inflection point there.