tmua.me Medium Set B Paper 2 · Question 14

A student attempts to prove that the equation $x^3-x=6$ has no positive real solution.

Suppose that $x>0$ is a solution.
Dividing the equation by $x$ gives $x^2-1=6x^{-1}$ .
Differentiating both sides with respect to $x$ gives $2x=-6x^{-2}$ .
The left-hand side is positive and the right-hand side is negative, which is a contradiction.
Therefore the equation has no positive real solution.

Which of the following best describes this attempt?

AThe first error is in line

\mathrm{I}

BThe first error is in line

\mathrm{II}

CThe first error is in line

\mathrm{III}

DThe first error is in line

\mathrm{IV}

EThe first error is in line

\mathrm{V}

FThe argument is correct.

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