For a continuous function

MATHEMATICS · Single correct · AP · Calculus AB · Integration and Accumulation of Change · Integration and Accumulation of Change

Problem

For a continuous function ff, the sign of ff on several intervals is given below: • f(x)<0f(x)<0 on (−3,0)(-3,0) • f(x)>0f(x)>0 on (0,4)(0,4) • f(x)<0f(x)<0 on (4,6)(4,6) Let g(x)=∫−3xf(t) dtg(x)=\int_{-3}^{x} f(t)\,dt. On which of the following intervals must gg be increasing? (a) (−3,0)(-3,0) (b) (−3,4)(-3,4) (c) (0,4)(0,4) (d) (0,6)(0,6)

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