Final answer:
To find the value of x for which y has its minimum value, we need to find the vertex of the quadratic function y = 60x + 3x² - 4x³. The value of x for which y has its minimum value is 3/8.
Step-by-step explanation:
To find the value of x for which y has its minimum value, we need to find the vertex of the quadratic function
y = 60x + 3x² - 4x³.
Since the coefficient of x³ is negative (-4), the graph of the function opens downward.
The x-coordinate of the vertex can be found using the formula x = -b/2a, where a, b, and c are the coefficients of the quadratic function.
In this case, a = -4, b = 3, and c = 60,
so x = -3/(2*(-4))
= 3/8.
Therefore, the value of x for which y has its minimum value is 3/8.