2020 ONE(c)

Merit
Question
Find the value of xx for which the graph of the function y=x1+lnxy = \dfrac{x}{1+\ln x} has a stationary point.

*You must use calculus and show any derivatives that you need to find when solving this problem.*
Official Answer
dydx=(1+lnx)1x1x(1+lnx)2\dfrac{dy}{dx}=\dfrac{(1+\ln x)\cdot 1-x\cdot \dfrac{1}{x}}{(1+\ln x)^2}

=lnx(1+lnx)2=\dfrac{\ln x}{(1+\ln x)^2}

dydx=0lnx=0\dfrac{dy}{dx}=0 \Rightarrow \ln x=0

x=1x=1
Grading Criteria

Achievement (u)

  • Correct derivative.

Merit (r)

  • Correct solution with correct derivative.

Excellence T1

-

Excellence T2

-
Video Explanation
NCEA Level 3 Calculus Differentiation 2020 NZQA Exam - Worked Answers by infinityplusone(starts at 4:11)
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