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Official 2017 Paper 1 · Q16

Paper 1Algebra

The functions ff and gg are given by f(x)=3x2+12x+4f(x)=3x^2+12x+4 and g(x)=x3+6x2+9x−8g(x)=x^3+6x^2+9x-8.

What is the complete set of values of xx for which one of the functions is increasing and the other decreasing?

Ax≥−1x\geq-1
Bx≤−1x\leq-1
C−3≤x≤−2,x≥−1-3\leq x\leq-2,\quad x\geq-1
Dx≤−2,x≥−1x\leq-2,\quad x\geq-1
Ex≤−3,−2≤x≤−1x\leq-3,\quad-2\leq x\leq-1
Fx≤−3,x≥−2x\leq-3,\quad x\geq-2
G−2≤x≤−1-2\leq x\leq-1

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