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

Explanation

Given `x+y=14 & S=x^{2}+y^{2}` where `y=14-x`



`therefore {S}={x}^{2}+(14-{x})^{2}={x}^{2}+14^{2}+{x}^{2}-28 {x}=2 {x}^{2}-28 {x}+14^{2}`



`frac{d s}{d x}=4 {x}-28 rightarrow(1)`



`frac{d s}{d x}=0 Rightarrow 4 {x}-28=0 Rightarrow {x}=7`



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