Final answer:
To determine the value of a, we need to find the derivative of the function and set it equal to zero. The derivative of the function y = ax^4 + 1/x is 4ax^3 - 1/x^2. To find the minimum, we set the derivative equal to zero. Solving for a, we find that a = 0.5387.
Step-by-step explanation:
To determine the value of a, we need to find the derivative of the function and set it equal to zero. The derivative of the function y = ax^4 + 1/x is 4ax^3 - 1/x^2. To find the minimum, we set the derivative equal to zero:
4ax^3 - 1/x^2 = 0
Simplifying the equation, we get:
4ax^5 - 1 = 0
Substituting x = 1.125 into the equation, we can solve for a:
4a(1.125)^5 - 1 = 0
Solving for a, we find that a = 0.5387.