2017 THREE(b)

Achievement

Question

Find the gradient of the curve

y = \frac{1}{x} - \frac{1}{x^2}

at the point

\left(2, \frac{1}{4}\right)

.

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

Official Answer

y=x^{-1}-x^{-2}

\dfrac{dy}{dx}=-x^{-2}+2x^{-3}

=\dfrac{-1}{x^2}+\dfrac{2}{x^3}

At

x=2

\dfrac{dy}{dx}=\dfrac{-1}{4}+\dfrac{2}{8}=0

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 51:02)

Exam Paper (2017)Assessment Schedule (2017)

Related Questions

2024 THREE(b)Achievement

The graph below shows the function $y = f(x)$. [DIAGRAM] (i) For the function above, find the valu...

2024 TWO(a)Achievement

A function is defined parametrically by the pair of equations: $x = 3t^2 + 1$ and $y = \cos t.$ Fi...

2024 ONE(b)Achievement

A curve is defined by the equation $y = (x^2 + 3x + 2)\,\sin x$. Find the gradient of the tangent t...

2024 THREE(a)Achievement

Differentiate $y = \sqrt{x}.\sec(6x)$. You do not need to simplify your answer....

2024 TWO(b)Achievement

An object is travelling in a straight line. Its displacement, in metres, is given by the formula $s...