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If xy(y-x) = 2a^(3), show that y has a m...

If `xy(y-x) = 2a^(3)`, show that y has a minimum value when x = a.

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AAKASH SERIES-MAXIMA AND MINIMA -Advanced Subjective Type Questions
  1. For what values of k, f(x) = x-(k)/(x) has a maximum value at x = -2.

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  2. If y = sum(i=1)^(n)(x-x(i))^(2), x(i) are constants, then for what val...

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  3. If xy(y-x) = 2a^(3), show that y has a minimum value when x = a.

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  4. Show that the least value of a^(2) sec^(2)x + b^(2) "cosec"^(2)x is (...

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  5. If x, y, k, m, n are positive and x + y = k, then find the maximum val...

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  6. Find the greatest and least value of (sin x)^((sin x)).

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  7. If x, y are positive real numbers such that xy = 1 then show that the ...

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  8. If the sum fo two positive numbers is 20 then show that the maximum va...

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  9. If the sum of two positive numbers is 48 then find the two numbers who...

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  10. The sum of two numbers is 20 . If the product of the square of one num...

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  11. A quadratic function in x has the value 9 when x = 1 and has a maximum...

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  12. If y = a log|x| + bx^(2) + x has extreme values at x = 2 and x = -4/3 ...

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  13. If y=(ax+b)/((x-1)(x-4)) has a maximum value at the point (2,-1) then

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  14. A cubic function of x has maximum 10 and minimum -5/2, when x = -3 and...

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  15. Find the triangle of the greatest area among the right triangles of a ...

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  16. The sum of the hypotenuse and one side of a right angled triangle is g...

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  17. Two sides of a triangle is given. If the area of a triangle is maximum...

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  18. If the perimeter of a rectangle is contant, then show that the rectang...

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  19. If the area of a rectangle is contant, then show that the rectangle be...

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  20. Find the area of greatest rectangle that can be inscribed in (x^(2))/(...

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