2019 ONE(d)

Merit
Question
For what value(s) of xx is the function y=x3exy = x^3 e^x decreasing?

You must use calculus and show any derivatives that you need to find when solving this
problem.
Official Answer
dydx=3x2ex+x3ex\dfrac{dy}{dx}=3x^2e^x+x^3e^x
=x2ex(3+x)=x^2e^x(3+x)

dydx<0\dfrac{dy}{dx}<0
⇒x2ex(3+x)<0\Rightarrow x^2e^x(3+x)<0

3+x<03+x<0
x<−3x<-3
Grading Criteria

Achievement (u)

  • Correct derivative.

Merit (r)

  • Correct solution with correct derivative.

Excellence T1

-

Excellence T2

-
Video Explanation
NCEA Level 3 Calculus Differentiation 2019 NZQA Exam - Worked Answers by infinityplusone(starts at 10:45)
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Exam Paper (2019)Assessment Schedule (2019)
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