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Prove that x^x has minimum value at x =1...

Prove that `x^x` has minimum value at x =`1/e`

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MODERN PUBLICATION-APPLICATION OF DERIVATIVES-EXERCISE
  1. Find the points of local maxima and local minima, if any, of the follo...

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  2. Find the points of local maxima and local minima, if any, of the follo...

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  3. Prove that x^x has minimum value at x =1/e

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  4. The curve y = (x^2 +ax+b)/(x-10) has a stationary point at (4,1). Find...

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  5. y = (ax-b)/((x-1)(x-4)) has a turning point P (2,-1). Find the values ...

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  6. Find two positive numbers whose sum is 14 and product is maximum.

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  7. Find two positive numbers whose sum is 16 and product is maximum.

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  8. Amongst all pairs of positive numbers with product 256 find those whos...

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  9. Amongst all pairs of positive numbers with product 64 find those whose...

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  10. Find two numbers whose sum is 15 and the square of one multiplied by t...

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  11. Find two positive numbers whose sum is 15 and the sum of whose squares...

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  12. Find two positive numbers 'x' and 'y' such that their sum is 35 and pr...

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  13. Find two positive numbers whose sum is 16 and whose sum of cubes is mi...

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  14. Find two positive numbers x and y such that x+y = 60 and xy^3 is maxim...

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  15. How should we choose two numbers, each greater than or equal to -2 who...

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  16. Find the maximum slope of the curve: y = -x^3 + 3x^2 + 2x - 27

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  17. If the sum of the lengths of hypotenuse and a side of a right-angled t...

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  18. A wire of length 36 m is to be cut into two pieces. One of the pieces ...

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  19. A wire of length 36 cm is cut into two pieces . One of the pieces is t...

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  20. Prove that the perimeter of a right-angled triangle of given hypotenus...

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