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The maximum value of x^(1/x),x >0 is...

The maximum value of `x^(1/x),x >0` is (a)`e^(1/e)` (b) `(1/e)^e` (c) `1` (d) none of these

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`f(x)=x^{\frac{1}{x}}`
Let `y=x^{\frac{1}{x}}`
Therefore,
`\log y=\log _{e} x` ...
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RD SHARMA-MAXIMA AND MINIMA-Solved Examples And Exercises
  1. Write the maximum value of f(x)=x^(1//x) .

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  2. Write the maximum value of f(x)=(logx)/x , if it exists.

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  3. The maximum value of x^(1/x),x >0 is (a)e^(1/e) (b) (1/e)^e (c)...

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  4. If a x+b/xgeqc for all positive x where a ,\ b ,\ >0 , then a b<(c^2)/...

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  5. The minimum value of x/((log)e x) is e (b) 1//e (c) 1 (d) none of thes...

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  6. For the function f(x)=x+1/x x=1 is a point of maximum (b) x=-1 is a p...

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  7. Let f(x)=x^3+3x^2-9x+2 . Then, f(x) has a maximum at x=1 (b) a minimum...

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  8. The minimum value of f(x)=x^4-x^2-2x+6 is (a) 6 (b) 4 (c) 8 (d) none o...

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  9. The number which exceeds its square by the greatest possible quanti...

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  10. Let f(x)=(x-a)^2+(x-b)^2+(x-c)^2 . Then, f(x) has a minimum at x= (a+...

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  11. The sum of two non-zero numbers is 8, the minimum value of the sum ...

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  12. The function f(x)=sum(r=1)^5(x-r)^2 assuming minimum value at x= ...

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  13. At x=(5pi)/6,\ \ f(x)=2sin3x+3cos3x is (a) 0 (b) maximum (c) minimum (...

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  14. If x lies in the interval [0,\ 1] , then the least value of x^2+x+1...

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  15. The least value of the function f(x)=x^3-18 x^2+96 x in the interval [...

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  16. The maximum value of f(x)=x/(4-x+x^2) on [-1,1] is (a)1/4 (b) -1/3...

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  17. Find the point on the curve y^2=4x which is nearest to the point (2, 1...

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  18. If x+y=8 , then the maximum value of x y is (a) 8 (b) 16 (c) 20 (d)...

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  19. The least and greatest values of f(x)=x^3-6x^2+9x in [0,\ 6] , are ...

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  20. f(x)=sin+sqrt(3)cosx is maximum when

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