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A farmer wants to construct a circular w...

A farmer wants to construct a circular well and a square garden in his field. He wants to keep sum of their permeters fixed. The prove that the sum of their area is least when the side of a square garden is double the radius of the circular well. Do you think good planning can save energy, time and money.

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The sum of the perimeter of a circle and square is k, where k is some constant. Prove that the sum of their areas is least when the side of square is double the radius of the circle.

MODERN PUBLICATION-APPLICATION OF DERIVATIVES-EXERCISE
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  3. A farmer wants to construct a circular well and a square garden in his...

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  6. Find the rate of change of the area of a circle with respect to its ra...

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  8. The interval in which y = x^2 e^-x is increasing is:

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  9. The slope of the normal to the curve y = 2x^2+3 sinx at x=0 is:

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  10. The line y = x+1, is a tangent to the curve y^2 = 4x at the point.

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  11. If f(x) = 3x^2+15x+5, then the approximate value of f (3.02) is :

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

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

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

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  16. A cylindrical tank of radius 10 m is being filled with wheat at the ra...

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  17. The slope of the tangent to the curve x = t^2+3t-8, y = 2t^2-2t-5at th...

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  18. The line y = mx +1, is a tangent to the curve y^2 = 4x if the value of...

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  19. The normal at the point (1,1) on the curve 2y + x^2 = 3 is:

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  20. The normal to the curve x^2 = 4y passing (1,2) is:

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