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

Solution

Let one number = x
$therefore space space space other space number space equals space 15 minus straight x Let space space straight S space equals space straight x squared plus left parenthesis 15 minus straight x right parenthesis squared space equals space 2 straight x squared minus 30 straight x plus 225 space space space space space dS over dx space equals space 4 straight x minus 30 space space space space space dS over dx space equals space 0 space space space gives space us space space 4 straight x minus 30 space equals space 0 space space space space space rightwards double arrow space space space straight x space equals space 15 over 2 space space space fraction numerator straight d squared straight S over denominator dx squared end fraction space equals space 4 At space straight x space equals space 15 over 2. space fraction numerator straight d squared straight S over denominator dx squared end fraction space equals space 4 comma space space space which space is space plus ve therefore space space space space space straight S space is space minimumn space when space space straight x space equals space 15 over 2 therefore space space space space one space number space equals space 15 over 2 space and space other space number space equals space 15 minus 15 over 2 space equals space 15 over 2$

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Application Of Derivatives

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

Some More Questions From Application of Derivatives Chapter

The radius of a circle is increasing uniformly at the rate of 4 cm per second Find the rate at which the area of the circle is increasing when the radius is 8 cm.

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