Find the smallest value of the function y = x^2-2x + 7

In order to find the smallest value of the function y = x ^ 2 – 2 * x + 7, you must first find its derivative. That is, we get:
Derivative y = (y) ‘= (x ^ 2 – 2 * x + 7)’ = (x ^ 2) ‘- (2 * x)’ + (7) ‘= 2 * x ^ (2 – 1) – 2 * 1 * x ^ (1 – 1) + 0 = 2 * x ^ 1 – 2 * x ^ 0 = 2 * x – 2 * 1 = 2 * x – 2;
Let us equate the derivative of the function to 0, and find its roots. That is, we get:
2 * x – 2 = 0;
2 * (x – 1) = 0;
x – 1 = 0;
We transfer the known values ​​to one side, and the unknown ones to the other side. When transferring values, their signs are changed to the opposite sign. That is, we get:
x = 0 + 1;
x = 1;
x min = 1;
Then, min = y (1) = 1 ^ 2 – 2 * 1 + 7 = 1 – 2 + 7 = – 1 + 7 = 6;
Answer: y min = 6.