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NDA 2017
Exam
NDA
Year
2017
Subject
Mathematics
Chapter
Trigonometric Ratios & Identities

NDA 2017 · Mathematics · Trigonometric Ratios & Identities

What is the maximum value of the function f(x)=4 ^2 x+1 ?

What is the maximum value of the function f(x)=4sin⁡2x+1?f(x)=4 \sin ^2 x+1 ?

Options

  1. A5
  2. B3
  3. C2
  4. D1

Correct answer

A. 5

Step-by-step solution

Weknow,We know,-1 \leq sin⁡x\sin x \leq 1 ⇒0≤sin⁡2x≤1⇒0≤4sin⁡2x≤4⇒1≤4sin⁡2x+1≤5\begin{aligned} & \Rightarrow 0 \leq \sin ^2 x \leq 1 \\ & \Rightarrow 0 \leq 4 \sin ^2 x \leq 4 \\ & \Rightarrow 1 \leq 4 \sin ^2 x+1 \leq 5 \end{aligned}
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