MATHEMATICS · Single correct · AP · Calculus AB · Integration and Accumulation of Change · Integration and Accumulation of Change
Problem
Let f be positive on an open interval containing x=1, and define
H(x)=∫g(x)5f(t)dt,
where g is differentiable on the interval and g′(1)>0. Which of the following statements about H′(1) is true?
(a) H′(1) is positive because it equals f(g(1))g′(1).
(b) H′(1) is negative because it equals −f(g(1))g′(1).
(c) H′(1) is zero because the upper limit of integration is constant.
(d) H′(1) is negative because it equals −f(1)g′(1).