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Euclid Sample Paper 2 · Q16

Paper 2Functions & graphs

A differentiable function f:R→Rf:\mathbb R\to\mathbb R is defined as wobbly if there exists a real number xx such that

f′(x)=0.f'(x)=0.

The function ff is known not to be wobbly and satisfies

f(−1)<0<f(1).f(-1)<0<f(1).

Which of the following functions must be wobbly?

  • I. g(x)=(f(x))2g(x)=(f(x))^2,
  • II. h(x)=f(x2−2x)+f(x2+2x)h(x)=f(x^2-2x)+f(x^2+2x),
  • III. k(x)=f(x3+x)k(x)=f(x^3+x).
Anone
BI only
CII only
DIII only
EI and II only
FI and III only
GII and III only
HI, II and III

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