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Question -

Show that f(x) =cos x is a decreasing function on (0, π), increasing in (–π, 0) and neitherincreasing nor decreasing in (–π, π).



Answer -

Given f(x) = cos x

 

 f’(x)= –sin x

Taking different region from 0 to 2π

Let x (0,π).

 Sin(x)> 0

 –sinx < 0

 f’(x)< 0

Thus f(x) is decreasing in (0, π)

Let x (–π,o).

 Sin(x) < 0

 –sinx > 0

 f’(x)> 0

Thus f(x) is increasing in (–π, 0).

Therefore, from above condition we find that

 f(x) is decreasing in (0, π) and increasing in (–π, 0).

Hence, condition for f(x) neither increasing nor decreasing in(–π, π)

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