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Prove that f(x)="sin"x-x is decreasing ...

Prove that `f(x)="sin"x-x` is decreasing `AAx inR`.

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BETTER CHOICE PUBLICATION-APPLICATIONS OF DERIVATIVES-ASSIGNMENT (SECTION III)
  1. Prove that f(x)="cos"x is strictly decreasing (0,pi)

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  2. f(x) = cos x is neither increasing nor decreasing in (0,2pi)

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  3. Prove that f(x)=x^(7)+3x^(5)+15 is increasing function.

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  4. Prove that f(x)=2/(x)+5 is strictly decreasing for all x inR,xne0.

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  5. Prove that f(x)="tan"x is strictly increasing in (-pi/(2),pi/(2))

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  6. Prove that f(x)="sin"x-x is decreasing AAx inR.

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  7. Determine the intervals in which the following functions f (x) = x^2 +...

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  8. Find the intervals in which the following functions are strictly incre...

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  9. Find the intervals in which the following functions are strictly incre...

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  10. Find the intervals in which the following functions are strictly incre...

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  11. Determine the intervals in which the following functions f (x ) = 2x^3...

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  12. Find the intervals in which the following functions are strictly incre...

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  13. Find the intervals in which the following functions are strictly incre...

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  14. Find the intervals in which the following functions are strictly incre...

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  15. Find the intervals in which the following functions are strictly incre...

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  16. Find the intervals in which the function : f (x) = 20 - 9x + 6x^2 - x^...

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  17. Find the intervals in which the following functions are strictly incre...

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  18. Find the intervals in which the following functions are strictly incre...

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  19. Find the intervals in which the following functions are strictly incre...

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  20. Find the intervals in which the following functions are strictly incre...

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