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Increasing & Decreasing Functions · Question 52 of 74

Question 52

EasyOriginal question

Which of these functions is strictly decreasing on (0,π2)\left(0, \frac{\pi}{2}\right)?

Options for question 52

Show the answer and explanation
CorrectNot quiteAnswer D

Correct answer: D

Explanation

  1. ddx(cos⁡x)=−sin⁡x\frac{d}{dx}(\cos x) = -\sin x, which is negative throughout (0,π2)\left(0, \frac{\pi}{2}\right).

  2. sin⁡x\sin x and tan⁡x\tan x rise there, and sin⁡2x\sin 2x rises up to π4\frac{\pi}{4} and falls after it.

Concept
Choosing a monotonic function
Typical time
60 s
Your time
—
The rule this testsTrigonometric functions
Practise this chapter →

Ten questions from Increasing & Decreasing Functions, at your own pace.

Practise this chapter →

Ten questions from Increasing & Decreasing Functions, at your own pace.