Increasing/decreasing intervals

Determine the ranges of x-values where a function is increasing or decreasing using the first derivative.

29 questions

WJEC Unit 1 Specimen Q16
16. Find the range of values of \(x\) for which the function $$f ( x ) = x ^ { 3 } - 5 x ^ { 2 } - 8 x + 13$$ is an increasing function.
SPS SPS SM Pure 2023 September Q2
6 marks
2.
\(f ( x ) = \frac { 1 - 2 x ^ { 9 } } { x ^ { 5 } } \quad\) for \(x > 0\) Prove that \(f ( x )\) is a decreasing function.
[0pt] [6 marks]
OCR MEI C2 2008 June Q4
4 Use calculus to find the set of values of \(x\) for which \(\mathrm { f } ( x ) = 12 x - x ^ { 3 }\) is an increasing function.
AQA AS Paper 2 Specimen Q8
6 marks
8 Prove that the function \(\mathrm { f } ( x ) = x ^ { 3 } - 3 x ^ { 2 } + 15 x - 1\) is an increasing function.
[0pt] [6 marks]