Find the value of x at which the function y = x ^ 2-28x + 211 reaches its minimum value.

Find the derivative of the function:

y ‘= (x ^ 2 – 2x + 211) = 2x – 2.

Let us equate it to zero and find the coordinates of the extrema:

2x – 2 = 0;

2x = 2;

x = 1.

Since at the point x0 = 1 the derivative changes its value from negative to positive, this point is the minimum of the function.

Answer: the function reaches its minimum value at the point x = 1.