2013 ONE(c)

Merit
Question
Find the xx values of any points of inflection on the graph of the function y=e(6−x2)y = e^{(6 - x^2)}.

Show any derivatives that you need to find when solving this problem.
Official Answer
dydx=−2xe6−x2\dfrac{dy}{dx}=-2xe^{6-x^2}

d2ydx2=−2e6−x2+4x2e6−x2\dfrac{d^2y}{dx^2}=-2e^{6-x^2}+4x^2e^{6-x^2}

Point of inflection when d2ydx2=0\dfrac{d^2y}{dx^2}=0

(4x2−2)e6−x2=0(4x^2-2)e^{6-x^2}=0

4x2−2=04x^2-2=0

x=±12x=\pm\dfrac{1}{\sqrt{2}}
Grading Criteria

Achievement (u)

  • Correct dydx\dfrac{dy}{dx}

Merit (r)

  • Correct solution with correct first and second derivatives.
  • ±\pm not required, accept positive answer only.

Excellence T1

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Excellence T2

-
Exam Paper (2013)Assessment Schedule (2013)
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