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Find two positive numbers x and y suc...

Find two positive numbers `x` and `y` such that `x+y=60` and `x y^3` is maximum.

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NCERT GUJARATI-APPLICATION OF DERIVATIVES-EXERCISE 6.5
  1. Find the maximum value of 2x^3-24 x+107in the interval [1, 3]. Find t...

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  2. It is given that at x=1 , the function x^4-62 x^2+a x+9 attains its ma...

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

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  4. Find two numbers whose sum is 24 and whose product is as large as p...

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  5. Find two positive numbers x and y such that x+y=60 and x y^3 is max...

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  6. Find two positive numbers x and y such that their sum is 35 and the ...

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  7. Find two positive numbers whose sum is 16 and the sum of whose cube...

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  8. A square piece of tin of side 18 cm is to be made into a box withou...

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  9. A rectangular sheet of tin 45 cm by 24 cm is to be made into a box ...

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  10. Show that of all the rectangles inscribed in a given fixed circle, ...

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

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  12. Of all the closed cylindrical cans (right circular), of a given vol...

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  13. A wire of length 28 m is to be cut into two pieces. One of the piec...

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  14. Prove that the volume of the largest cone that can be inscribed in a ...

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  15. Show that the right-circular cone of least curved surface and given...

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  16. Show that the semi-vertical angle of the cone of the maximum volume a...

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

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  18. The point on the curve x^2=2ywhich is nearest to the point (0, 5) is(A...

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

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  20. The maximum value of [x(x-1)+1]^(1/3),0lt=xlt=1is(A) (1/3)^(1/3) (B) ...

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