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Show that f(x) = (1)/((1 + x^(2))) is in...

Show that `f(x) = (1)/((1 + x^(2)))` is increasing for all `x le 0`

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`f'(x) = - (1 + x^(2))^(-2) .2x = (-2x)/((1 + x^(2))^(2)) ge 0 " when " x le 0`
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RS AGGARWAL-APPLICATIONS OF DERIVATIVES-Exercise 11G
  1. Show that f(x) = (x - (1)/(x)) is increasing for all x in R, where x !...

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  2. Show that f(x) = ((3)/(x) + 5) is decreasing for all x in R, where x !...

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  3. Show that f(x) = (1)/((1 + x^(2))) is increasing for all x le 0

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  4. Show that f(x) = (x^(3) + (1)/(x^(3))) is decreasing on [-1, 1]

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  5. Show that f(x) = (x)/(sinx) is increasing on [0, (pi)/(2)]

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  6. Prove that the following functions are strictly increasing: f(x)=log(1...

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  7. Let I be an interval disjointed from [-1,\ 1] . Prove that the functio...

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  8. Show that f(x) = ((x -2))/((x +1)) is increasing for all x in R, excep...

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  9. Find the intervals in which the function f given by f(x)=2x^2-3xis(a) ...

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  10. Find the intervals in which the function f given by f(x)=2x^3-3x^2-36 ...

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  11. Find the intervals on which the function f(x) = 6 - 9x - x^(2) is (a) ...

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  12. Find the intervals in which the function f(x)=x^4-(x^3)/3 is increasin...

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  13. Find the intervals in which the function "f\ "("x")="\ x"^3-"\ "12"...

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  14. Find the intervals on which each of the following functions is (a) inc...

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  15. Find the intervals in which f(x)=6+12 x+3x^2-2x^3 is increasing or dec...

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  16. Find the intervals on which each of the following functions is (a) inc...

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  17. Find the intervals in which f(x)=(x-1)(x-2)^2 is increasing or decreas...

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  18. Find the intervals in which f(x)=x^4-4x^3+4x^2+15 is increasing or dec...

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  19. Find the intervals on which each of the following functions is (a) inc...

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  20. Determine the intervals in which the function f(x)=x^4-8x^3+22 x^2-24 ...

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