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NDA 2021
Exam
NDA
Year
2021
Subject
Mathematics
Chapter
Application of Derivatives

NDA 2021 · Mathematics · Application of Derivatives

Consider the following statements in respect of the function f(x)=...

Consider the following statements in respect of the function f(x)=sin⁡xf(x)=\sin x : 1. f(x)f(x) increases in the interval (0,π)(0, \pi). 2. f(x)f(x) decreases in the interval \left(\frac{5 \pi}{2}, 3 \pi\right)$. Which of the above statements is/are correct?

Options

  1. A11 only
  2. B22 only
  3. CBoth 11 and 22
  4. DNeither 11 nor 22

Correct answer

B. 22 only

Step-by-step solution

f(x)=sin⁡xGraph of f(x)=sin⁡x from x∈[0,2π]\begin{aligned} & f(x)=\sin x \\ & \text{Graph of } f(x)=\sin x \text{ from } x \in[0,2 \pi]\end{aligned} Here, f(x)=sin⁡xf(x)=\sin x, Increases from \left[0, \frac{\pi}{2}\right]and[3π2,2π]and \left[\frac{3 \pi}{2}, 2 \pi\right] decreases from \left[\frac{\pi}{2}, \frac{3 \pi}{2}\right]Hence(1)isnotcorrect.Hence (1) is not correct.\text{ Domain }= \left[\frac{5 \pi}{2},3 \pi\right]= \left[2 $pi+π2,2\$pi+\frac{\pi}{2}, 2\pi+\pi\right]= \left[\frac{\pi}{2}, \pi\right]Fromgraph,sin⁡(x)From graph, \sin (x) decreases from \left[π2\frac{\pi}{2} , \pi\right]Hence, (2) is correct.
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