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Prove that the function f(x)=cosx is nei...

Prove that the function `f(x)=cosx` is neither increasing nor decreasing in `(0,\ 2pi)`

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Verified by Experts

We have given
`f(x)=cosx`
`f′(x)=−sinx`
As ,
`x in(0,pi)`
`impliessinx`>`0`
`implies−sinx`<`0`
`impliesf′(x)`<`0`
...
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RD SHARMA-INCREASING AND DECREASING FUNCTION -Solved Examples And Exercises
  1. Prove that the function f(x)=cosx is strictly decreasing in (0,\ pi)

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  2. Prove that the function f(x)=cosx is strictly increasing in (pi,\ 2pi)

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  3. Prove that the function f(x)=cosx is neither increasing nor decreas...

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  4. Show that f(x)=x^2-xsinx is an increasing function on (0,\ pi//2) .

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  5. Find the value(s) of a for which f(x)=x^3-a x is an increasing functio...

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  6. Find the values of b for which the function f(x)=sinx-b x+c is a decre...

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  7. Show that f(x)=x+cosx-a is an increasing function on R for all values ...

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  8. Let f defined on [0, 1] be twice differentiable such that | f"(x)| ...

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  9. Find the intervals in which f(x)=x|x|,\ \ x in R is increasing or dec...

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  10. Find the intervals in which f(x)=sinx+|sinx|,\ \ 0<xlt=2pi is increasi...

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  11. Find the intervals in which f(x)=s in\ x(1+cosx),\ \ 0<x<pi/2 is incre...

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  12. What are the values of ' a ' for which f(x)=a^x is increasing on R

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  13. What are the values of ' a ' for which f(x)=a^x is decreasing on R

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  14. Write the set of values of ' a ' for which f(x)=(log)a x is increasing...

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  15. Write the set of values of ' a ' for which f(x)=(log)a x is decreasing...

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  16. Find ' a ' for which f(x)=a\ (x+sinx)+a is increasing on R .

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  17. Find the values of ' a ' for which the function f(x)=sinx-a x+4 is inc...

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  18. Find the set of values of ' b ' for which f(x)=b(x+cosx)+4 is decreasi...

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  19. Find the set of values of ' a ' for which f(x)=x+cosx+a x+b is increas...

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  20. Write the set of values of k for which f(x)=k x-sinx is increasing on ...

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