Find the value of x at which the function y=x^2-7x^2+15x has the greatest value
To find the value of x at which the function y = x^2 – 7x^2 + 15x has the greatest value, we need to determine the vertex of the quadratic function.
The general form of a quadratic function is y = ax^2 + bx + c, where a, b, and c are constants.
In this case, the quadratic function is y = x^2 – 7x^2 + 15x. Comparing it to the general form, we have a = 1, b = -7, and c = 15.
The x-coordinate of the vertex of a quadratic function can be found using the formula x = -b / (2a). Plugging in the values, we get:
x = -(-7) / (2 * 1) = 7 / 2 = 3.5
So, the value of x at which the function has the greatest value is x = 3.5.