Let be differentiable on

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

Problem

Let ff be differentiable on R\mathbb R. Define Q(x)=∫x3f(t) dt+∫3xx2f(t) dtQ(x)=\displaystyle\int_{x}^{3} f(t)\,dt+\int_{3x}^{x^{2}} f(t)\,dt. Which of the following gives Q′(x)Q'(x)? (a) −f(x)+2x f(x2)+3 f(3x)-f(x)+2x\,f\big(x^{2}\big)+3\,f\big(3x\big) (b) f(x)+2x f(x2)−3 f(3x)f(x)+2x\,f\big(x^{2}\big)-3\,f\big(3x\big) (c) −f(x)+2x f(x2)−3 f(3x)-f(x)+2x\,f\big(x^{2}\big)-3\,f\big(3x\big) (d) −f(x)+f(x2)−3 f(3x)-f(x)+f\big(x^{2}\big)-3\,f\big(3x\big)

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