2021 ONE(b)

Achievement
Question
The graph below shows the function y=f(x)y = f(x).
Loading diagram...
For the function above:

(i) Find the value(s) of xx that meet the following conditions:

(1) f′(x)=0f'(x) = 0:

(2) f(x)f(x) is concave upwards:

(ii) What is the value of lim⁡x→7f(x)\lim_{x \to 7} f(x):

State clearly if the value does not exist.
Official Answer
(1) x<2x<2, x=4x=4
(2) 3<x<63<x<6
(ii)
33
Grading Criteria

Achievement (u)

  • 2 out of 3 correct responses.

Merit (r)

-

Excellence T1

-

Excellence T2

-
Video Explanation
NCEA Level 3 Calculus Differentiation 2021 NZQA Exam - Worked Answers by infinityplusone(starts at 3:13)
Subscribe
Exam Paper (2021)Assessment Schedule (2021)
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(d)Merit

Find the $x$-value(s) of any stationary points on the graph of the function below, and determine the...

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....