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Find the intervals in which the function...

Find the intervals in which the function `f(x)=(4x^(2)+1)/x` is decreasing

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The correct Answer is:
`-1/2 lt x lt 1/2` and `x ne 0` when `x in (-1/2, 0) uu (0, 1/2)`
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CHHAYA PUBLICATION-INCREASING AND DECREASING FUNCTION-Illustrative Examples
  1. Show that the function (x^(3)-3x^(2)+4x) increases with x.

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  2. Find the intervals in which the function f(x)=(4x^(2)+1)/x is increasi...

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  3. Find the intervals in which the function f(x)=(4x^(2)+1)/x is decreasi...

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  4. Find the range of values of x for which the function f(x)=2x^(3)-9x^(2...

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  5. Find the range of values of x for which the function f(x)=2x^(3)-9x^(2...

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  6. If f(x)=10-9x+6x^(2)-x^(3), examine whether f(x) increases or decrease...

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  7. If f(x)=10-9x+6x^(2)-x^(3), examine whether f(x) increases or decrease...

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  8. If f(x)=10-9x+6x^(2)-x^(3), examine whether f(x) increases or decrease...

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  9. Find the intervals in which the function f given by f(x)=x^(3)+1/x^(3)...

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  10. Find the intervals in which the function f given by f(x)=x^(3)+1/x^(3)...

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  11. Show that, for 0 lt theta lt pi/2, (sin theta)/theta steadily decrease...

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  12. Find the intervals in which the function f given by f(x)=sin x + cos x...

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  13. Find the intervals in which the function f given by f(x)=sin x + cos x...

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  14. Find the intervals in which the function f(x)=x^(x) (x gt 0) is increa...

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  15. Find the intervals in which the function f(x)=x^(x) (x gt 0) is decrea...

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  16. Show that f(x)=tan^(-1)(cos x+sin x) is a stictly increasing function ...

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  17. Prove that the function f(x)=x^(3)-x^(2) is neither increasing nor dec...

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  18. Find the intervals in which the function f(x)=(x+1)^(3)(x-3)^(3) is in...

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  19. Find the intervals in which the function f(x)=(x+1)^(3)(x-3)^(3) is de...

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  20. Sparate the interval [0, pi/2] into sub-intervals in which f(x)=sin^(4...

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