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Show that the maximum value of (1/x)^x i...

Show that the maximum value of `(1/x)^x` is `e^(1/e)dot`

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NAGEEN PRAKASHAN-APPLICATIONS OF DERIVATIVES-Exercise 6f
  1. Find the values of x for which the following functions are maximum or ...

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  2. Find the maximum or minimum values of the following functions: (i)x^...

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  3. For what values of x, the function f(x) = x^(5)-5x^(4)+5x(3)-1 is maxi...

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  4. Find the maximum and minimum values of the function f(x) = sin x + cos...

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  5. Find the maximum and minimum values of the function f(x) = x+ sin 2x, ...

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  6. Find the maximum and minimum values of the function f(x) = (sin x)/(1+...

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  7. Show that s in^p\ theta\ cos^q\ theta attains a maximum, when theta...

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  8. Find the maximum value of the function (log x)/x " when "x gt 0.

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  9. Find the maximum value of the function x^(1//x).

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  10. Show that the maximum value of (1/x)^x is e^(1/e)dot

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  11. Show that the function x^(3)- 3x^(2)+3x+1 has neither a maxima nor a m...

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  12. Show that f(x)=sinx(1+cosx) is maximum at x=pi/3 in the interval [0,\ ...

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  13. If the function f(x) = x^(3)-24x^(2)+6kx-8 is maximum at x = 2. Then, ...

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  14. Prove that value of the function xy(y-x)=2a^3 is minimum at x=a.

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  15. Show that the function(-x^(2) log x) is minimum at x= 1/sqrte.

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  16. Find the maximum value of the function x * e^(-x).

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  17. Show that the maximum value of the function sqrt2(sin x+ cos x) is 2.

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  18. Show that the maximum and minimum values of the function (x+1)^2/(x+3)...

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  19. If the function y = ae^(x) + bx^(2)+3x is maximum at x = 0 and minimum...

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