NCEA Calculus 2021 ONE(c - Solution & Explanation

Question

A curve has the equation

y = (2x + 3)e^{x^2}

.

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

y=(2x+3)e^{x^2}

\dfrac{dy}{dx}=2e^{x^2}+(2x+3)(2x)e^{x^2}

\dfrac{dy}{dx}=2e^{x^2}(1+x(2x+3))

\dfrac{dy}{dx}=2e^{x^2}(2x^2+3x+1)

\dfrac{dy}{dx}=0

for stationary points.

2e^{x^2}=0

has no solutions since

2e^{x^2}>0

2x^2+3x+1=0

x=-\dfrac{1}{2}

or

x=-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 2021 NZQA Exam - Worked Answers by infinityplusone(starts at 8:07)

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2021 ONE(c)

Achievement (u)

Merit (r)

Excellence T1

Excellence T2