Find the largest or smallest value of the function: y = -x ^ 2 + 5x

In order to find the smallest value of the function y = x ^ 2 + 5 * x, you must first find its derivative. That is, we get:
Derivative y = (y) ‘= (x ^ 2 + 5 * x)’ = (x ^ 2) ‘+ (5 * x)’ + (7) ‘= 2 * x ^ (2 – 1) – 5 * 1 * x ^ (1 – 1) = 2 * x ^ 1 – 5 * x ^ 0 = 2 * x – 5 * 1 = 2 * x – 5;
Let us equate the derivative of the function to 0, and find its roots. That is, we get:
2 * x – 5 = 0;
We transfer the known values ​​to one side, and the unknown ones to the other side. When transferring values, their signs change to the opposite sign. That is, we get:
2 * x = 0 + 5;
2 * x = 5;
x = 5/2;
x min = 5/2;
Then, min = y (5/2) = (5/2) ^ 2 + 5 * 5/2 = 25/4 + 25/2 = 25/4 + 50/4 = 75/4;
y max = – b / (2 * a) = – 5 / (2 * 1) = – 5/2;
Answer: y min = 75/4 and y max = – 5/2.