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

September 28, 2021 | education

| 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.

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