NCEA Calculus 2020 TWO(c - Solution & Explanation

Question

Find the

x

-coordinates of any stationary points on the graph of the function

f(x) = (2x - 3)e^{x^2 + k}

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

Official Answer

f'(x)=(2x-3)2xe^{x^2+k}+2e^{x^2+k}

=e^{x^2+k}((2x-3)2x+2)

=e^{x^2+k}(4x^2-6x+2)

=2e^{x^2+k}(2x^2-3x+1)

f'(x)=0\Rightarrow 2e^{x^2+k}=0

or

2x^2-3x+1=0

2e^{x^2+k}

has no solutions since

2e^{x^2+k}

is always positive.

2x^2-3x+1=0

(2x-1)(x-1)=0

x=\frac{1}{2}

or

x=1

Grading Criteria

-

-

Video Explanation

NCEA Level 3 Calculus Differentiation 2020 NZQA Exam - Worked Answers by infinityplusone(starts at 23:51)

2020 TWO(c)