2021 THREE(b)

Achievement

Question

The graph of the function

y = 4\sqrt{x} - x + 2

, where

x > 0

, has a stationary point at point Q.

Find the coordinates of point Q.

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

Official Answer

\dfrac{dy}{dx}=\dfrac{2}{\sqrt{x}}-1

At stationary point, derivative

=0

\dfrac{2}{\sqrt{x}}=1

x=4

Coordinates are

(4,6)

Grading Criteria

Achievement (u)

Correct solution with correct derivative.

Merit (r)

Excellence T1

Excellence T2

Video Explanation

NCEA Level 3 Calculus Differentiation 2021 NZQA Exam - Worked Answers by infinityplusone(starts at 57:36)

Exam Paper (2021)Assessment Schedule (2021)