Let for all real

MATHEMATICS · Single correct · AP · Calculus AB · Analytical Applications of Differentiation · Analytical Applications of Differentiation

Problem

Let f(x)=x3−6x2+9xf(x)=x^{3}-6x^{2}+9x for all real xx, and define F(x)=∫0xf(t) dtF(x)=\displaystyle \int_{0}^{x} f(t)\,dt. On which of the following intervals is FF concave up? (a) (1,∞)(1,\infty) (b) (−∞,1)(-\infty,1) (c) (−∞,1)∪(3,∞)(-\infty,1)\cup(3,\infty) (d) (1,3)(1,3)

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