01 - 04 Number Problems in Maxima and Minima

Problem 1
What number exceeds its square by the maximum amount?

Solution 1

 

Problem 2
What positive number added to its reciprocal gives the minimum sum?

Solution 2

 

Problem 3
The sum of two numbers is k. Find the minimum value of the sum of their squares.

Solution 3

 

Problem 4
The sum of two numbers is k. Find the minimum value of the sum of their cubes.

Solution 4

 
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