2017 ONE(b)

Achievement

Question

Find the gradient of the tangent to the curve

y = \dfrac{e^{2x}}{x + 2}

at the point where

x = 0

.

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

Official Answer

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

At

x=0

\dfrac{dy}{dx}=\dfrac{2\times 2-1}{4}=\dfrac{3}{4}

Grading Criteria

Achievement (u)

Correct solution with correct derivative.

Merit (r)

-

Excellence T1

-

Excellence T2

-

Video Explanation

NCEA Level 3 Calculus Differentiation 2017 NZQA Exam - Worked Answers by infinityplusone(starts at 1:42)

Exam Paper (2017)Assessment Schedule (2017)

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