Answer:
Minimum: 5, 5
Maximum: 9, 1
Step-by-step explanation:

The sum of the squares would be


Differentiating with respect with x

Equating with zero

Double derivative of f(x)


So, at
the value of the function is minimum.
Therefore, at
and
the function has minimum value of 
For the finding the maximum values of
and
we have to use trial and error method




0 and 10 will not be considered as 0 is neither positive nor negative.
So the maximum value of the numbers is 9 and 1 and the maximum value of the function is 82.