2021 THREE(c)

Excellence

Question

For what values of

x

is the function

y = \dfrac{x}{x^2 + 4}

increasing?

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

Official Answer

\dfrac{dy}{dx}=\dfrac{(x^2+4)-x(2x)}{(x^2+4)^2}

=\dfrac{4-x^2}{(x^2+4)^2}

Increasing when

\dfrac{dy}{dx}>0

\dfrac{4-x^2}{(x^2+4)^2}>0

4-x^2>0

-2<x<2

Grading Criteria

Achievement (u)

Correct $\dfrac{dy}{dx}$

Merit (r)

Correct $\dfrac{dy}{dx}$ and identifies $-2$ and $2$ as the boundaries of the interval required.

Excellence T1

T1: Correct solution with correct derivative.

Excellence T2

-

Video Explanation

NCEA Level 3 Calculus Differentiation 2021 NZQA Exam - Worked Answers by infinityplusone(starts at 60:53)

Exam Paper (2021)Assessment Schedule (2021)

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