2021 TWO(b)

Achievement

Question

A curve has the equation

y = \dfrac{x^2}{x+1}

.

Find the

x

-coordinate(s) of any stationary point(s) on the curve.

*You must use calculus and show any derivatives that you need to find when solving this problem.*

Official Answer

\dfrac{dy}{dx}=\dfrac{(x+1)2x-x^2}{(x+1)^2}

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

\dfrac{dy}{dx}=0\Rightarrow x(x+2)=0

x=0

x=-2

Grading Criteria

Achievement (u)

Correct solutions with correct derivative.

Merit (r)

Excellence T1

Excellence T2

Video Explanation

NCEA Level 3 Calculus Differentiation 2021 NZQA Exam - Worked Answers by infinityplusone(starts at 33:24)

Exam Paper (2021)Assessment Schedule (2021)