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Separate the intervals of monotonocity f...

Separate the intervals of monotonocity for the function `f(x)=x^2e^(-x)`

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BANSAL-APPLICATION OF DERIVATIVE-All Questions
  1. Find intervals of monotonicity of function : f(x)=(|x-1|)/(x^2)

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  2. If g(x)=f(x)+f(1-x) and f prime prime (x)< 0; 0 <= x <= 1. show that g...

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  3. Separate the intervals of monotonocity for the function f(x)=x^2e^(-x)

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  4. Compute the intervals of monotonicity for the following f(x)=x+ln(...

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  5. Find value of a so that f(x)=a x-s in x\ is monotonic

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  6. Prove that f(x)=2/3x^9-x^6+2x^3-3x^2+6x-1 is always increasing.

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  7. Find least and greatest value of f(x)=e^x^(2-4x+3)\ in [-\ 5,5]

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  8. Find the image of interval [-1,3] under the mapping specified by...

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  9. Find the range of the following functions f(x)=\ sqrt(x-3)+2sqrt(5-...

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  10. Find the range of the following function f(x)=(x^4-x^2-2x+8)/(x^4-x...

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  11. Prove that 2sinx+tanx\ geq3x\ \ (0lt=x<pi/2)

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  12. Find the set of values of x for which the inequality In(1+x)>x/(1+x) ...

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  13. Show that ln\ (1+x)> x-(x^2)/2\ AA\ x\ in (0,oo)

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  14. Show that the equation x^5-3x-1=0\ has a unique root in [1,2] .

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  15. Prove that x/(1+x)>ln(1+x)< x AA x>0

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  16. f( x )=cos3x−15cosx+8  in  [ π/ 3 , 3π/ 2 ] is increasing or ...

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  17. Use the function f(x)=x^(1/x),x >0, to determine the bigger of the two...

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  18. Prove that e^x-e^(-x)-2x >0\ AA\ x > 0. Hence, prove that e^x+e^...

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  19. prove that the function f(x)=(lnx)/x , is strictly decreasing in...

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  20. Verify Rolles Theorem for f(x)=(sin x)/(e^x)\ in\ [0,pi]\ \ \ \ ...

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