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Beyond Horizon Set 4 Paper 1 · Q11

Paper 1Algebra

The functions ff and gg are given by f(x)=4x2+10x+5f(x)=4x^2+10x+5 and g(x)=x3+5x2+8x−10g(x)=x^3+5x^2+8x-10.

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

Here increasing and decreasing mean that the derivatives at the point are strictly positive and strictly negative, respectively.

Ax<−2or−43<x<−54x<-2\quad\text{or}\quad-\frac43<x<-\frac54
Bx≤−2x\leq-2
C−4≤x≤−3-4\leq x\leq-3, x≥−2x\geq-2
Dx≤−3x\leq-3, x≥−2x\geq-2
Ex≤−4x\leq-4, −3≤x≤−2-3\leq x\leq-2
Fx≤−4x\leq-4, x≥−3x\geq-3
G−3≤x≤−2-3\leq x\leq-2

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