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

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MODERN PUBLICATION-APPLICATION OF DERIVATIVES-EXERCISE
  1. Find two positive numbers whose sum is 15 and the sum of whose squares...

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

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

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

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

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

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

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

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

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

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  11. Prove that the area of right-angled triangle of given hypotenuse is ma...

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  12. Prove that the least perimeter of an isosceles triangle in which a cir...

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  13. Show that, of all the rectangles with a given area, the square has the...

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  14. Show that rectangle of maximum perimeter, which can be inscribed in a ...

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  15. Show that of all rectangles inscribed in a given circle the square has...

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  16. A rectangle is inscribed in a semi-circle of radius 'r' with one of it...

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  17. Of all rectangles , each of which has perimeter: 40 cm . Find the one ...

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  18. Of all rectangles , each of which has perimeter: 60 cm . Find the one ...

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  19. An open box with a square base is to be made out of a given iron sheet...

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  20. Show that the semi-vertical angle of the cone of the maximum volume an...

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