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Prove that the function f(x)=x+1/x (x ne...

Prove that the function `f(x)=x+1/x (x ne 0)` is decreasing for all x in `(-1, 0) uu (0, 1)`.

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CHHAYA PUBLICATION-INCREASING AND DECREASING FUNCTION-Exercise 15 : Short Answer Type Questions
  1. Find the intervals in which the function f(x)=3/x+x/3 is increasing

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  2. Find the intervals in which the function f(x)=3/x+x/3 is decreasing

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  3. Prove that the function f(x)=x+1/x (x ne 0) is decreasing for all x in...

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  4. Find the intervals in which the following functions are (a) increasing...

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  5. Find the intervals in which the following functions are (a) increasing...

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  6. Find the intervals in which the following functions are (a) increasing...

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  7. 24. Find the intervals in which the following function is (a) increasi...

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  8. 24. Find the intervals in which the following function is (a) increasi...

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  9. Find the intervals in which the following functions are (a) increasing...

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  10. Find the intervals in which the function f(x)=sin x-cos x where 0 lt x...

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  11. Find the intervals in which the function f(x)=sin x-cos x where 0 lt x...

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  12. Prove that the function f(x)=x^(3)-6x^(2)+12 x-18 is increasing for al...

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  13. Prove that the function f(x)=x^2-x+1 is neither increasing nor decr...

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  14. Find the intervals in which f(x)=2x^3-24 x+7 is increasing or decreasi...

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  15. If f(x)=(x-1) e^(x)+1, show that f(x) is positive for all positive val...

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  16. Prove that, the function 5+24x+3x^(2)-x^(3) increases in the interval ...

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  17. If f(theta)=theta sin theta+cos theta, show that, f(theta) steadily in...

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  18. Find the intervals in which f(x)=(x+2) e^(-x) is increasing

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  19. Find the intervals in which f(x)=(x+2) e^(-x) is decreasing

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  20. Find the intervals in which f(x)=(x-1)^3(x-2)^2 is increasing or decre...

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