Find two positive numbers whose sum is 14 and the sum of whose squares is minimum.

Explanation

let `x` and `y` be numbers

such that `x+y=14`

Let S be sum of squares of x and y

Let `S` be the sum of the squares of `x` and `y`.

`S={x}^{2}+{y}^{2} `

`S={x}^{2}+(14-{x})^{2}`

`S=2 {x}^{2}-28 {x}+196 `

`frac{{dS}}{{dx}}=4 {x}-28`

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