For a continuous function defined on an interval containing
MATHEMATICS · Single correct · AP · Calculus AB · Integration and Accumulation of Change · Integration and Accumulation of Change
Problem
For a continuous function f defined on an interval containing a, let F(x)=∫axf(t)dt. Which of the following statements is always true?
(a) If F is decreasing at x=c, then f(c)>0.
(b) If f is decreasing on an interval, then F is decreasing on that interval.
(c) If f(x)>0 on an interval, then F is increasing on that interval.
(d) If f(x)<0 at x=c, then F has a local minimum at c.