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

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PRADEEP PUBLICATION-APPLICATIONS OF DERIVATIVES-EXERCISE
  1. . Find two numbers whose sum is 24 and whose product is as large as po...

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

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

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  4. A square ·piece of tin of side 12 cm is to be made into a box without ...

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  5. A rectangular sheet of tin 45 cm x 24 cm is to be made into a box with...

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

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  7. Show that the rectangle of maximm area that can be inscribed in a circ...

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  8. Show that the right circular cylinder of given surface and maximum vol...

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  9. If all the closed cylindrical cans (right circular), which enclose a g...

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  10. A wire of length 28 m is to be cut into two pieces, one of the pieces ...

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  11. Prove that volume of largest cone, which can be inscribed in a sphere,...

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  12. Show that the right circular cone of least curved surface and given vo...

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

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  14. Show that semi-vertical angle of right circular cone of given surface ...

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  15. The point on the curve x^2 = 2y which is nearest to the point (0,5) is...

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  16. For all real values of x, the minimum value of (1-x+x^2)/(1+x+x^2 is:

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  17. The maximum value of [x(x-1)+1]^(1/3), 0lexle1 is:

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  18. Using differentials, find an approximate value of each of the followin...

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  19. Using differentials, find an approximate value of each of the followin...

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  20. Show that the function given by f(x) = (logx)/x has maximum at x=e

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