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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`

A

e

B

`e^e`

C

`e^(1//e)`

D

`(1//e)^(1//e)`

Text Solution

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The correct Answer is:
C
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OBJECTIVE RD SHARMA ENGLISH-MAXIMA AND MINIMA -Exercise
  1. Investigate for the maxima and minima of the function f(x)=int1^x[2(t...

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  2. If the function f(x) = x^3 + 3(a-7)x^2 +3(a^2-9)x-1 has a positive ...

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

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  4. If the function f(x)=2x^3-9ax^2+12a^2x+1, where a gt 0, attains its m...

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  5. The maximum distance of the point (k,0) from the curve 2x^(2) +y^(2)...

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  6. A cubic function f(x) vanishes at x=-2 and has relative minimum/maximu...

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  7. An isosceles triangle of vertical angle 2theta is inscribed in a ...

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  8. Find minimum value of px+qy where p>0, q>0, x>0, y>0 when xy=r,^2 with...

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  9. The maximum slope of curve y =-x^(3)+3x^(2)+9x-27 is

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  10. If (x+c)/(1+x^2) where c is a constant , then when y is stationary , x...

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  11. N Characters of information are held on magnetic tape, in batches of x...

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  12. Statement I If A gt 0 , B gt 0 and A+B= pi/3, then the maximum value o...

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  13. The largest value of 2x^(3)-3x^(2)-12x+5 for -2 le x le 2 occurs when

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  14. The first and second order derivatives of a function f(x) exit at all ...

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  15. The minimum value of 2^(x^2-3)^(3) +27 is 2^(27) (b) 2 (c) 1 (d) ...

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  16. Let f(x) =cosx sin2x. Then , min (f(x):-pilexlepi) is

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  17. If f(x)=sin^6x+cos^6x , then which one of the following is false

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  18. The value of a for which the function f(x)=asinx+(1/3)sin3x has an ext...

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  19. If ax+b/x >= c for all positive x, where a, b, c > 0, then-

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  20. The greatest value of f(x)=cos(x e^([x])+7x^2-3x),x in [-1,oo], is (wh...

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