Which listed interval is entirely an interval of increase?

01 / Standard#Your turn

f(x)=5\cos(x+\pi/3)

Official paper · jm01-2024 · I.12 · PDF 3

Skills and prerequisite lessons

Option A $(0,\pi/2)$
Option B $(\pi/2,\pi)$
Option C $(\pi,3\pi/2)$
Option D $(3\pi/2,2\pi)$
Option E $(\pi/3,5\pi/6)$

Working and explanation

BUILD THE REASONING

Hint 1

Cosine increases when its argument lies between π and 2π.

Hint 2

Shift that interval left by π/3.

Worked solution

Find one complete increasing interval.
$\pi<x+\pi/3<2\pi\iff2\pi/3<x<5\pi/3$
Only option C lies wholly inside this interval.
$(\pi,3\pi/2)\subset(2\pi/3,5\pi/3)$

Checks and common pitfalls: An option that overlaps an increasing interval is insufficient.

Reasoning checklist · self / teacher assessment

Teaching assessment checklist, independently authored. Use the original paper for official marks.
Find one complete increasing interval.
$\pi<x+\pi/3<2\pi\iff2\pi/3<x<5\pi/3$
Only option C lies wholly inside this interval.
$(\pi,3\pi/2)\subset(2\pi/3,5\pi/3)$

Think first. Reveal a hint when the class is ready.

2024 JM01