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Prove that the function f(x)=x^(3)-x^(2)...

Prove that the function `f(x)=x^(3)-x^(2)` is neither increasing nor decreasing in `-2/3 lt x lt 2/3`.

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CHHAYA PUBLICATION-INCREASING AND DECREASING FUNCTION-Illustrative Examples
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  4. Find the intervals in which the function f given by f(x)=sin x + cos x...

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

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

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

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

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

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

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

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

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  14. Find the intervals in which the function f(x)=log (1+x) -x/(1+x) is in...

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  15. Find the intervals in which the function f(x)=log (1+x) -x/(1+x) is de...

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  16. If x gt 0, show that, x gt log (1+x) gt x-x^(2)/2.

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  17. Let y=3x.(x+a)/(x+b)+5 [a and b are positive constants and a gt b] be ...

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  18. Use the function f(x)=x^(1/x), x gt 0, to determine the bigger of the ...

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  19. let h(x)=f(x)-[f(x)]^(2)+[f(x)]^(3) for every real number x. Prove tha...

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  20. The function f(x) =tan^(-1)(sinx+cosx) is an increasing function in

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