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# The sum of two positive numbers is $16$. What is the smallest possible value of the sum of their squares?

## The smallest possible value of the sum of their squares is $128 .$

Derivatives

Differentiation

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##### Heather Z.

Oregon State University

##### Samuel H.

University of Nottingham

##### Michael J.

Idaho State University

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### Video Transcript

okay, Giving two values experts. Why that? Add up to 16? We know we can write this in terms of why as Weigel 16 minus x Not taking the derivative shoe X squared minus 32 acts was 250. Sex click. We said the derivative four acts, minus 32 said equal to zero gives us axe equals eight eight squared plus eight square gives A 64 was 64 which gives us our minimum value of 128.

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