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tmua.me Medium Set E Paper 2 · Q13

Paper 2CalculusAlgebra

A student gives the following argument about

f(x)=x−1x,x≠0.f(x)=x-\frac1x,\qquad x\ne0.
  1. Differentiating gives f′(x)=1+1x2f'(x)=1+\dfrac1{x^2}.
  2. Hence f′(x)>0f'(x)>0 for every nonzero real number xx.
  3. Therefore, for any nonzero real numbers a<ba<b, we have f(a)<f(b)f(a)<f(b).
  4. It follows that the equation f(x)=0f(x)=0 has at most one real solution.

Which of the following best describes the argument?

AThe first error is in line I.
BThe first error is in line II.
CThe first error is in line III.
DThe first error is in line IV.
EThe argument is completely correct.

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