2020 THREE(b)

Achievement
Question
For what value(s) of xx does the tangent to the graph of the function

f(x)=2x−2x, x>0f(x)=2x-2\sqrt{x},\ x>0, have a gradient of 1?

You must use calculus and show any derivatives that you need to find when solving this
problem.
Official Answer
f(x)=2x−2xf(x)=2x-2\sqrt{x}

f′(x)=2−x−12f'(x)=2-x^{-\frac{1}{2}}

⇒2−1x=1\Rightarrow 2-\dfrac{1}{\sqrt{x}}=1

1x=1\dfrac{1}{\sqrt{x}}=1

x=1x=1
Grading Criteria

Achievement (u)

  • Correct value of xx with correct derivative

Merit (r)

-

Excellence T1

-

Excellence T2

-
Video Explanation
NCEA Level 3 Calculus Differentiation 2020 NZQA Exam - Worked Answers by infinityplusone(starts at 42:13)
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Exam Paper (2020)Assessment Schedule (2020)
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