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Let f(x)=x- sinx. Find the intervals o...

Let f(x)=x- sinx. Find the intervals of monotonicity.

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`f'(x) =1 -cos x`
Now f'(x) `gt`0 every where except at `x=0 ,+- 2pi +- 4pi` etc. But all these points are discrete (countble) and do not form an interval. Hence we can conclude that f(x) is stricitly increasing in R. In fact we can also see it graphically.
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RESONANCE-APPLICATION OF DERIVATIVES-High Level Problems (HLP)
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  2. Find the interval in which f(x) = xsqrt(4ax-x^2), (alt0) is decreasing

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  3. f: [0.4]-> R is a differentiable function. Then prove that for some a,...

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  19. For what real values of a' and 'b' all the extrema of the function f(x...

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