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Show that the function given by f(x) = sin x is a. strictly increasing in (0,π2) b. strictly decreasing in (π2,π) c. neither increasing nor decreasing in (0, π) - Mathematics

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Question

Show that the function given by f(x) = sin x is

  1. strictly increasing in `(0, pi/2)`
  2. strictly decreasing in `(pi/2, pi)`
  3. neither increasing nor decreasing in (0, π)
Sum
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Solution

The given function is f(x) = sin x.

f'(x) = cos x

a. Since for each `x in (0, pi/2)`, cos x > 0, we have f'(x) > 0

Hence, f is strictly increasing in `(0. pi/2)`

b. Since for each `x in (pi/2 , pi), cos x < 0` we have f'(x) < 0

Hence, f is strictly decreasing in `(pi/2, pi)`

c.  From the results obtained in (a) and (b), it is clear that f is neither increasing nor decreasing in (0, π).

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Chapter 6: Application of Derivatives - Exercise 6.2 [Page 205]

APPEARS IN

NCERT Mathematics Part 1 and 2 [English] Class 12
Chapter 6 Application of Derivatives
Exercise 6.2 | Q 3 | Page 205

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